In questions 1 to 10, there are four options, out of which one is correct.
1. Comparison of parts of a whole may be done by a
(a) Bar graph (b) pie chart (c) linear graph (d) line graph
In questions 1 to 10, there are four options, out of which one is correct.
1. Comparison of parts of a whole may be done by a
(a) Bar graph (b) pie chart (c) linear graph (d) line graph
Explanation:
(b) Pie chart
In the above given question, we have to choose the correct option from the given options.
We know that, to compare anything we use the pie chart, because it represents the whole circle as a part.
2. A graph that displays data that changes continuously over periods of time is
(a) Bar graph (b) pie chart (c) histogram (d) line graph
2. A graph that displays data that changes continuously over periods of time is
(a) Bar graph (b) pie chart (c) histogram (d) line graph
Explanation:
(d) Line graph
In the above given question, we have to choose the correct option from the given options.
We know that, when the data changes continuously with the time, it will give us a straight line.
So, we can say that, a line graph will represent the continuous change with the time.
3. In the given graph, the coordinates of point x are
(a) (0, 2) (b) (2, 3) (c) (3, 2) (d) (3, 0)
3. In the given graph, the coordinates of point x are
(a) (0, 2) (b) (2, 3) (c) (3, 2) (d) (3, 0)
Explanation:
(c) (3, 2)
In the above given question, we have to choose the correct option from the given options.
We know that, to find the co-ordinate of any point we have to draw the perpendicular line from that point to both the axis.
So, by drawing the perpendicular line on x-axis we get 3 and by drawing perpendicular line on y-axis we get 2.
Therefore, the coordinate of x can be written as (3, 2)
4. In the given graph, the letter that indicates the point (0, 3) is
(a) P (b) Q (c) R (d) S
4. In the given graph, the letter that indicates the point (0, 3) is
(a) P (b) Q (c) R (d) S
Explanation:
(c) R
In the above given question, we have to choose the correct option from the given options.
We know that, to find any point on the graph from the co-ordinate, we have to locate both the point on their respective axis and then draw the horizontal line from the y-axis and vertical line from the x-axis.
Now, here point on the x-axis is 0 and y-axis is 3, so drawing perpendicular we get the point as R.
5. Point (3, 4) is at a distance of
(a) 3 from both the axis (b) 4 from both the axis
(c) 4 from the x axis and 3 from y axis (d) 3 from x axis and from y axis
5. Point (3, 4) is at a distance of
(a) 3 from both the axis (b) 4 from both the axis
(c) 4 from the x axis and 3 from y axis (d) 3 from x axis and from y axis
Explanation:
(c) 4 from the x-axis and 3 from y-axis
In the above given question, we have to choose the correct option from the given options.
We know that, to find any point on the graph from the co-ordinate, we have to locate both the point on their respective axis and then draw the horizontal line from the y-axis and vertical line from the x-axis.
Now, here point (3,4) means, it is 3 on the x-axis and 4 on the y-axis.
6. A point which lies on both the axis is __________
(a) (0, 0) (b) (0, 1) (c) (1, 0) (d) (1, 1)
6. A point which lies on both the axis is __________
(a) (0, 0) (b) (0, 1) (c) (1, 0) (d) (1, 1)
Explanation:
(a) (0,0)
In the above given question, we have to choose the correct option from the given options.
We know that, (0,0) is the intersection point of both the x-axis and y-axis.
So, this is the only point which lies on both the axis.
7. The coordinates of a point at a distance of 3 units from the x-axis and 6 units from the y-axis is
(a) (0, 3) (b) (6, 0) (c) (3, 6) (d) (6, 3)
7. The coordinates of a point at a distance of 3 units from the x-axis and 6 units from the y-axis is
(a) (0, 3) (b) (6, 0) (c) (3, 6) (d) (6, 3)
Explanation:
(d) (6, 3)
In the above given question, we have to choose the correct option from the given options.
We know that, while writing any co-ordinate, the first thing in the bracket represents the x-axis and the second term represent the y-axis.
So, here it is given that, distance on the x-axis is 6 unit and on the y-axis is 3 units.
Hence, we can write the co-ordinate as (6, 3).
8. In the given figure, the position of the book on the table may be given by
(a) (7, 3) (b) (3, 7)
(c) (3, 3) (d) (7, 7)
8. In the given figure, the position of the book on the table may be given by
(a) (7, 3) (b) (3, 7)
(c) (3, 3) (d) (7, 7)
Explanation:
(b) (3, 7)
In the above given question, we have to choose the correct option from the given options.
We know that, to find the co-ordinate of any point we have to draw the perpendicular line from that point to both the axis.
So, by drawing the perpendicular line on x-axis we get 3 and by drawing perpendicular line on y-axis we get 7.
Therefore, the coordinate of book can be written as (3, 7).
9. Data was collected on a student’s typing rate, and the graph was drawn as shown below. Approximately how many words had this student typed in 30 seconds?
(a) 20 (b) 24 (c) 28 (d) 34
9. Data was collected on a student’s typing rate, and the graph was drawn as shown below. Approximately how many words had this student typed in 30 seconds?
(a) 20 (b) 24 (c) 28 (d) 34
Explanation:
(c) 28
In the above given question, we have to choose the correct option from the given options.
Here, we have to find the number of words, so to find ther number of words we have given the time which is 30 second.
Now, draw a vertical line on the x-axis at a distance of 30 second and obtain a point on the straight line.
As we have obtained the point on the straight line, draw a horizontal line from that point to the y-axis, so we get another point on the y-axis.
Now, the point we get on the y-axis, is our answer, we get 28 words.
10. Which graphs of the following represent the table below?
10. Which graphs of the following represent the table below?
Explanation:
(d)
In the above given question, we have to choose the correct option from the given options.
We know that, to find any point on the graph from the co-ordinate, we have to locate both the point on their respective axis and then draw the horizontal line from the y-axis and vertical line from the x-axis.
So, here by putting the values given into the table, we get a straight line starting from the co-ordinate (1,4) to the co-ordinate (5,20).
In questions 11 to 25, fill in the blanks to make the statements true.
11.__________ displays data that changes continuously over periods of time.
In questions 11 to 25, fill in the blanks to make the statements true.
11.__________ displays data that changes continuously over periods of time.
Explanation:
Line Graph
We know that, when the data changes continuously with the time, it will give us a straight line.
So, we can say that, a line graph will represent the continuous change with the time.
12. The relation between dependent and independent variables is shown through a __________.
12. The relation between dependent and independent variables is shown through a __________.
Explanation:
Graph
We know that, graph is the best way to show the relation between the dependent variables and the independent variables.
13. We need __________ coordinates to represent a point on the graph sheet.
13. We need __________ coordinates to represent a point on the graph sheet.
Explanation:
two (a pair)
We know that, to represent any point on the graph, we should have both the co-ordinates that is x-coordinate and y-coordinate.
14. A point in which the x-coordinate is zero and the y-coordinate is nonzero will lie on the _________
14. A point in which the x-coordinate is zero and the y-coordinate is nonzero will lie on the _________
Explanation:
y-axis
We know that, to represent any point on the graph, wee should have both the co-ordinate.
Now, if one co-ordinate is zero, then the point will lie on the axis which is having nn-zero co-ordinate.
So, here, y-coordinate is non-zero, then the point will lie on the y-axis.
15. The horizontal and vertical lines in a line graph are usually called
__________ and __________.
15. The horizontal and vertical lines in a line graph are usually called
__________ and __________.
Explanation:
x-axis and y-axis
We know that, graph sheet is made of vertical and horizontal lines.
In the graph sheet, vertical lines referred as y-axis and horizontal lines are referred as x-axis.
16. The process of fixing a point with the help of the coordinates is known as __________ of the point.
16. The process of fixing a point with the help of the coordinates is known as __________ of the point.
Explanation:
Plotting
We know that, to plot a point, first we have to fix the co-ordinates of the point.
So, this process is known as plotting.
17. The distance of any point from the y-axis is the __________ coordinate.
17. The distance of any point from the y-axis is the __________ coordinate.
Explanation:
x coordinate
We know that, both the axis is perpendicular to each other.
So, to find the distance of any point from the y-axis, we have to find the x-coordinate.
x-coordinate will give us the distance of the point from the y-axis.
18. All points with y-coordinate as zero lies on the __________.
18. All points with y-coordinate as zero lies on the __________.
Explanation:
x-axis
We know that, when all the y-coordinates are zero, means all the point having only x-axis.
So, all the points will lie on the x-axis.
19. For point (5, 2), the distance from the x-axis is __________ units.
19. For point (5, 2), the distance from the x-axis is __________ units.
Explanation:
2 units.
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and y represents the distance on the y-axis from the x-axis.
So, the distance from the x-axis for the point (5,2) is 2.
20. The x-coordinate of any point lying on the y-axis will be __________.
20. The x-coordinate of any point lying on the y-axis will be __________.
Explanation:
zero (0)
We know that, when the x-coordinates are zero, means the point having only y-axis.
So, the x-coordinate will be zero.
21. The y-coordinate of the point (2, 4) is __________.
21. The y-coordinate of the point (2, 4) is __________.
Explanation:
4 units.
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and y represents the distance on the y-axis from the x-axis.
So, the y-coordinate of the point (2,4).
22. In the point (4, 7), 4 denotes the __________.
22. In the point (4, 7), 4 denotes the __________.
Explanation:
x- coordinate.
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and known as x-coordinate and y represents the distance on the y-axis from the x-axis and known as y-coordinate.
Here, for the point (4,7), 4 denotes the x-coordinate of the point.
23. A point has 5 as its x – coordinate and 4 as its y–coordinate. Then the coordinates of the point are given by __________.
23. A point has 5 as its x – coordinate and 4 as its y–coordinate. Then the coordinates of the point are given by __________.
Explanation:
(5, 4)
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and known as x-coordinate and y represents the distance on the y-axis from the x-axis and known as y-coordinate.
So, x-coordinate is 5 and y-coordinate is 4 can be written as (5,4).
24. In the coordinates of a point, the second number denotes the
__________.
24. In the coordinates of a point, the second number denotes the
__________.
Explanation:
y coordinate
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and known as x-coordinate and y represents the distance on the y-axis from the x-axis and known as y-coordinate.
25. The point where the two axes intersect is called the __________.
25. The point where the two axes intersect is called the __________.
Explanation:
Origin (0, 0)
We know that, graph sheet is made up of two lines, one is vertical know as y-axis and the second is horizontal known as x-axis.
Now, the intersection of both the line takes place at the point (0,0) which is known as origin of the graph sheet.
In questions 26 to 34, state whether the statements are true (T) or false (F).
26. For fixing a point on the graph sheet, we need two coordinates.
In questions 26 to 34, state whether the statements are true (T) or false (F).
26. For fixing a point on the graph sheet, we need two coordinates.
Explanation:
True
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and known as x-coordinate and y represents the distance on the y-axis from the x-axis and known as y-coordinate.
27. A line graph can also be a whole unbroken line.
27. A line graph can also be a whole unbroken line.
Explanation:
False
We know that, when a whole line is unbroken, it is called a linear graph.
28. The distance of any point from the x-axis is called the x-coordinate.
28. The distance of any point from the x-axis is called the x-coordinate.
Explanation:
False
We know that, point is represented by (x,y) form.
In this bracket, y represents the distance on the y-axis from the x-axis and known as y-coordinate.
29. The distance of the point (3, 5) from the y-axis is 5.
29. The distance of the point (3, 5) from the y-axis is 5.
Explanation:
False
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and known as x-coordinate.
So, here, x-coordinate is 3 not 5.
30. The ordinate of a point is its distance from the y-axis.
30. The ordinate of a point is its distance from the y-axis.
Explanation:
False
We know that, point is represented by (x,y) form.
In this bracket, y represents the distance on the y-axis from the x-axis and known as y-coordinate.
31. In the point (2, 3), 3 denotes the y-coordinate.
31. In the point (2, 3), 3 denotes the y-coordinate.
Explanation:
True
We know that, point is represented by (x,y) form.
In this bracket, y represents the distance on the y-axis from the x-axis and known as y-coordinate.
(2, 3) = (x-coordinate, y-coordinate)
32. The coordinates of the origin are (0, 0).
32. The coordinates of the origin are (0, 0).
Explanation:
True
We know that, graph sheet is made up of two lines, one is vertical know as y-axis and the second is horizontal known as x-axis.
Now, the intersection of both the line takes place at the point (0,0) which is known as origin of the graph sheet.
33. Points (3, 5) and (5, 3) represent the same point.
33. Points (3, 5) and (5, 3) represent the same point.
Explanation:
False
Here, points given to us are (3,5) and (5,3)
Now, in both the point, the distances from the x-axis and y-axis are not same.
The distance from the y-axis for first point is 3 and for second point it is 5.
In the same way, distance from the x-axis for the first point is 5 and for the second point is 3.
So, distances for both the points are not same.
Hence, both the point doesn’t represent the same point.
34. The y-coordinate of any point lying on the x-axis will be zero.
34. The y-coordinate of any point lying on the x-axis will be zero.
Explanation:
True
We know that, when the x-coordinates are zero, means the point having only y-coordinates.
Which means, the point will lie on the y-axis.
(5, 0) and (7, 0), when these points are plotted in the graph, both points will lie on the x-axis.
35. Match the coordinates given in Column A with the items mentioned
in Column B.
35. Match the coordinates given in Column A with the items mentioned
in Column B.
Explanation:
(1) Here, the x-coordinate is zero and y-coordinate is 5.
Which means, the distance of the point from the x-axis is 5.
(2) Here, the x-coordinate is 2 and y-coordinate is 3.
Which means, the distance of the point from the y-axis is 2.
(3) Here, the x-coordinate is 4 and y-coordinate is 8.
Which means, the y-coordinate is double of x-coordinate.
(4) Here, the x-coordinate is 3 and y-coordinate is 7.
Which means, the y coordinate is 2 × x – coordinate + 1.
(5) Here, the x-coordinate is 0 and y-coordinate is 0.
Which means, this are the co-ordinates of origin.
(6) Here, the x-coordinate is 5 and y-coordinate is 0.
Which means, only the y-coordinate is zero.
36. Match the ordinates of the points given in Column A with the items mentioned in Column B.
36. Match the ordinates of the points given in Column A with the items mentioned in Column B.
Explanation:
Here, x coordinate represents the abscissa and y coordinate represents the ordinate.
37. From the given graph, choose the letters that indicate the location of the points given below.
(a) (2, 0) (b) (0, 4) (c) (5, 1) (d) (2, 6) (e) (3,3)
37. From the given graph, choose the letters that indicate the location of the points given below.
(a) (2, 0) (b) (0, 4) (c) (5, 1) (d) (2, 6) (e) (3,3)
Explanation:
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and known as x-coordinate and y represents the distance on the y-axis from the x-axis and known as y-coordinate.
A indicates the points: (0, 4)
B indicates the points: (1, 5)
C indicates the points: (2, 6)
D indicates the points: (0, 2)
E indicates the points: (3, 3)
F indicates the points: (2, 0)
38. Find the coordinates of all letters in the graph given below.
38. Find the coordinates of all letters in the graph given below.
Explanation:
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and known as x-coordinate and y represents the distance on the y-axis from the x-axis and known as y-coordinate.
A Coordinates = (0, 7.5)
B Coordinates = (4, 5)
C Coordinates = (7.5, 2.5)
D Coordinates = (11, 0)
E Coordinates = (14.5, 6.5)
F Coordinates = (18, 9.5)
39. Plot the given points on a graph sheet.
(a) (5, 4) (b) (2, 0) (c) (3, 1) (d) (0, 4) (e) (4,5)
39. Plot the given points on a graph sheet.
(a) (5, 4) (b) (2, 0) (c) (3, 1) (d) (0, 4) (e) (4,5)
Explanation:
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and known as x-coordinate and y represents the distance on the y-axis from the x-axis and known as y-coordinate.
Now, draw the x and y axis, and plot the given points.
Points given to us are A = (5, 4), B = (2, 0), C = (3, 1), D = (0, 4) and E = (4, 5)
40. Study the given map of a zoo and answer the following questions.
(a) Give the location of the lions in the zoo.
(b) (D, f) and (C, d) represent the locations of which animals in the zoo.
(c) Where are the toilets located?
(d) Give the location of the canteen.
40. Study the given map of a zoo and answer the following questions.
(a) Give the location of the lions in the zoo.
(b) (D, f) and (C, d) represent the locations of which animals in the zoo.
(c) Where are the toilets located?
(d) Give the location of the canteen.
Explanation:
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and known as x-coordinate and y represents the distance on the y-axis from the x-axis and known as y-coordinate.
(a) From the graph, we can say that, the location of the lions in the zoo is (A, f)
(b) From the graph, we can say that, the point (D, f) and (C, d) represent the locations of the Monkey and elephant, respectively
(c) From the graph, we can say that, the toilets are located in (0, e)
(d) From the graph, we can say that, the location of the canteen is (C, c)
41. Write the x -coordinate (abscissa) of each of the given points.
(a) (7, 3) (b) (5, 7) (c) (0, 5)
41. Write the x -coordinate (abscissa) of each of the given points.
(a) (7, 3) (b) (5, 7) (c) (0, 5)
Explanation:
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and known as x-coordinate.
We also know that; x-axis is also known as abscissa.
So, the abscissa of the above given points is
(a) (7, 3) – 7
(b) (5, 7) – 5
(c) (0, 5) – 0
42. Write the y-coordinate (ordinate) of each of the given points.
(a) (3, 5) (b) (4, 0) (c) (2, 7)
42. Write the y-coordinate (ordinate) of each of the given points.
(a) (3, 5) (b) (4, 0) (c) (2, 7)
Explanation:
We know that, point is represented by (x,y) form.
In this bracket, y represents the distance on the y-axis from the x-axis and known as y-coordinate.
We also know that; y-axis is also known as ordinate.
So, the ordinate of the above given points is
(a) (3, 5) – 5
(b) (4, 0) – 0
(c) (2, 7) – 7
43. Plot the given points on a graph sheet and check if the points lie on a straight line. If not, name the shape they form when joined in the given order.
(a) (1, 2), (2, 4), (3, 6), (4, 8).
(b) (1, 1), (1, 2), (2, 1), (2, 2).
(c) (4, 2), (2, 4), (3, 3), (5, 4).
43. Plot the given points on a graph sheet and check if the points lie on a straight line. If not, name the shape they form when joined in the given order.
(a) (1, 2), (2, 4), (3, 6), (4, 8).
(b) (1, 1), (1, 2), (2, 1), (2, 2).
(c) (4, 2), (2, 4), (3, 3), (5, 4).
Explanation:
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and known as x-coordinate and y represents the distance on the y-axis from the x-axis and known as y-coordinate.
(a) Now, for the given points, (1, 2), (2, 4), (3, 6), (4, 8), we can plot the graph as given below
From the graph, we can say that, by joining all the points, we obtained a straight line.
(b) Now, for the given points, (1, 1), (1, 2), (2, 1), (2, 2), we can plot the graph as given below
From the graph, we can say that, by joining all the points, we obtained a square not a straight line.
(c) Now, for the given points, (4, 2), (2, 4), (3, 3), (5, 4), we can plot the graph as given below
From the graph, we can say that, by joining all the points, we do not obtain a straight line. But after joining the point A and D we get a triangle.
44. If y–coordinate is 3 times x -coordinate, form a table for it and draw a graph.
44. If y–coordinate is 3 times x -coordinate, form a table for it and draw a graph.
Explanation:
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and known as x-coordinate and y represents the distance on the y-axis from the x-axis and known as y-coordinate.
From the question, we can write y = 3x
Now, let’s suppose that the values of x are 1, 2, 3, 4
So, the corresponding y-coordinate values for the supposed x can be written as:
When x = 1, y= 3(1) = 3 ⇒ (1, 3)
When x = 2, y= 3(2) = 6 ⇒ (2, 6)
When x = 3, y= 3(3) = 9 ⇒ (3, 9)
When x = 4, y= 3(4) = 12 ⇒ (4, 12)
Hence, the obtained points are:
(1, 3), (2, 6), (3, 9) and (4, 12)
Now, plotting the graph for the obtained values of x and y-coordinates.
The graph for the above-given points is:
From the graph, we can say that, by joining all the points, we obtained a straight line.
45. Make a line graph for the area of a square as per the given table
Is it a linear graph?
45. Make a line graph for the area of a square as per the given table
Is it a linear graph?
Explanation:
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and known as x-coordinate and y represents the distance on the y-axis from the x-axis and known as y-coordinate.
From the given table, we can write the co-ordinates as,
(1, 1), (2, 4), (3, 9), (4, 16)
Now, from this co-ordinate we can draw the graph,
Here, in the above graph, x-axis represent the side og the square and y-axis represent the area of the square.
From the graph, we can see that the line is not lenear.
Hence, it is not a linear graph.
46. The cost of a notebook is Rs. 10. Draw a graph after making a table showing the cost of 2, 3, 4 … Notebooks. Use it to find
(a) The cost of 7 notebooks.
(b) The number of notebooks that can be purchased with Rs 50.
46. The cost of a notebook is Rs. 10. Draw a graph after making a table showing the cost of 2, 3, 4 … Notebooks. Use it to find
(a) The cost of 7 notebooks.
(b) The number of notebooks that can be purchased with Rs 50.
Explanation:
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and known as x-coordinate and y represents the distance on the y-axis from the x-axis and known as y-coordinate.
Now, the cost of one notebook is Rs.10
So, let’s take x-coordinate as the number of books and y-coordinate as the prize of books.
(a) Hence, the cost of 7 notebooks is 7×10 = 70 rs
(b) To find the number of notebooks that can be purchased for Rs. 50 is
= 50/10
= 5
Hence, the number of notebooks for Rs. 50 is 5.
47. Explain the situations represented by the following distance-time graphs.
47. Explain the situations represented by the following distance-time graphs.
Explanation:
(a) Here, the graph is drawn by taking time and distance.
So, by seeing the graph, we can say that the distance increases time also increases with equal intervals
(b) Here, the graph is drawn by taking time and distance.
So, by seeing the graph, we can say that the distance increases as time also increases but after some time distance will remains same for the increase in the time.
(c) Here, the graph is drawn by taking time and distance.
So, by seeing the graph, we can say that the distance increases times also increases by unequal intervals.
48. Complete the given tables and draw a graph for each.
(a)
(b)
48. Complete the given tables and draw a graph for each.
(a)
(b)
Explanation:
(a)
Here, values of x-coordinates are given and the equation to find the y-coordinate is also given.
y = 3x+1
So, by simply putting the values of x in the equation of y we get the values of y-coordinates.
x= 0, then y = 1
x=1, then y = 4
x= 2 and x = 3
x= 2, y = 3(2) +1 = 7
x= 3, y = 3(3) +1 = 10
Hence, the obtained coordinate points are:
(0, 1), (1, 4), (2, 7) and (3, 10)
Now, putting all the obtained co-ordinates on the graph,
(b)
Here, values of x-coordinates are given and the equation to find the y-coordinate is also given.
y = x-1
So, by simply putting the values of x in the equation of y we get the values of y-coordinates.
x= 1, then y = 0
Now, we have to find the value of y when x= 2, 4, 6,
x= 2, y = 2 -1 = 1
x= 4, y = 4- 1 = 3
x= 6, y = 6- 1 = 5
Hence, the obtained coordinate points are:
(1, 0), (2, 1), (4, 3) and (6, 5)
Now, putting all the obtained co-ordinates on the graph,
49. Study the given graphs (a) and (b) and complete the corresponding tables below
(a)
(b)
49. Study the given graphs (a) and (b) and complete the corresponding tables below
(a)
(b)
Explanation:
(a)
Here, we are given a graph and from that graph we have to find the value of y-coordinates corresponding to x-coordinates.
Now, the value of x-coordinates is given as 0,1,2 and 3.
So, let’s take x = 1, so to find the value of y-coordinate draw a line parallel to the y-axis at 1, and check whether where it cuts the graph.
So, we get y=1
Now, repeat the same process for all the other values of x.
Hence, the coordinates obtained are as follows:
(b)
Here, we are given a graph and from that graph we have to find the value of y-coordinates corresponding to x-coordinates.
Now, the value of x-coordinates is given as 0,1,2,3 and 4.
So, let’s take x = 1, so to find the value of y-coordinate draw a line parallel to the y-axis at 1, and check whether where it cuts the graph.
So, we get y=4
Now, repeat the same process for all the other values of x.
Hence, the coordinates obtained are as follows:
50. Draw a graph for the radius and circumference of a circle using a suitable scale.
(Hint: Take radius = 7, 14, 21 units and so on)
From the graph,
(a) Find the circumference of the circle when the radius is 42 units.
(b) At what radius will the circumference of the circle be 220 units?
50. Draw a graph for the radius and circumference of a circle using a suitable scale.
(Hint: Take radius = 7, 14, 21 units and so on)
From the graph,
(a) Find the circumference of the circle when the radius is 42 units.
(b) At what radius will the circumference of the circle be 220 units?
Explanation:
We know that, point is represented by (x,y) form.
In this bracket, x represents the distance on the x-axis from the y-axis and known as x-coordinate and y represents the distance on the y-axis from the x-axis and known as y-coordinate.
Now, let’s take radius on the x-axis and the circumference of the circle on the y-axis.
Here, we have to take the circumference, we know that the circumference of the circle is 2Ï€r.
So, from this relationship we can obtain the equation for the y.
y = 2Ï€x
now, find the value of y for all the given value of x which is 0,7,14 and 21.
When x= 0, then y = 2Ï€ (0) = 0
When x= 7, then y = 2Ï€ (7) = 44
When x= 14, then y = 2Ï€ (14) = 88
When x= 21, then y = 2Ï€ (21) = 132
Hence, the coordinates obtained are as follows:
(0, 0), (7, 44, (14, 88) and (21, 132)
Now, plot all the co-ordinate on the graph sheet,
(a)
Here, we have to find the value of y-coordinate when the x-coordinate is 42.
Now draw a vertical line on the 42 and from where it intersects the curve draw a horizontal line to get the value of y.
So, when the radius is 42 units, the value of y (circumference) is 264
(b)
Here, we have to find the value of x-coordinate when the value of y-coordinate is 220.
Now, draw a horizontal line on 220 and from where it intersects the curve draw a vertical line to get the value of x.
So, when the circumference is 220, the value of the radius is 35 units.
