1. How will you describe the position of a table lamp on your study table to another person?
1. How will you describe the position of a table lamp on your study table to another person?
Explanation:
In order to describe the position of the table lamp on the desk, we take two lines, one vertical and one horizontal. If the table is considered as a plane (x-axis and y-axis), the vertical line is the y-axis, the horizontal line is the x-axis, and a corner of the table is the origin where the X- and Y-axes intersect. Now the length of the table is the Y axis and the width is the X axis. Starting from the origin, connect the line to the table lamp and mark a point. The distances of the points to the X and Y axes must be calculated and then written as coordinates.
The distance from this point to the X and Y is x and y respectively, so the table lamp will be in (x,y) coordinates.
Here, (x, y) = (10, 20).
2. (Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city in your notebook. Represent the roads/streets by single lines.
There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North-South direction and another in the East-West direction. Each cross street is referred to in the following manner: If the 2nd street running in the North-South direction and 5th in the East-West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
(i) how many cross-streets can be referred to as (4, 3)?
(ii) how many cross-streets can be referred to as (3, 4)?
2. (Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city in your notebook. Represent the roads/streets by single lines.
There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North-South direction and another in the East-West direction. Each cross street is referred to in the following manner: If the 2nd street running in the North-South direction and 5th in the East-West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
(i) how many cross-streets can be referred to as (4, 3)?
(ii) how many cross-streets can be referred to as (3, 4)?
Explanation:
According to question, the graph is drawn below. The two main roads are N-S and W-E (North-South and West-East) are drawn. Five different parallel streets are drawn vertical and horizontal to main roads (assuming 1 cm = 200 m).
(i) Only one cross-street can be referred to as (4, 3), because 4th street is running along the North-South direction and 3rd street is running along West-East direction and these streets are intersecting at (4, 3) as shown below
.
(ii) Only one cross-street can be referred to as (3, 4), because 3rd street is running along the North-South direction and 4th street is running along West-East direction and these streets are intersecting at (3, 4) as shown below.
3. Write the answer to each of the following questions.
(i) What is the name of the horizontal and vertical lines drawn to determine the position of any point in the Cartesian plane?
(ii) What is the name of each part of the plane formed by these two lines?
(iii) Write the name of the point where these two lines intersect.
3. Write the answer to each of the following questions.
(i) What is the name of the horizontal and vertical lines drawn to determine the position of any point in the Cartesian plane?
(ii) What is the name of each part of the plane formed by these two lines?
(iii) Write the name of the point where these two lines intersect.
Explanation:
(i) The names of the horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane are called x-axis and y-axis, respectively.
(ii) The name of each part of the plane formed by these two lines (x-axis and y-axis) is called quadrants.
(iii) The point where these two lines (x-axis and y-axis) intersect is called the origin.
4. See Fig.3.14, and write the following.
i. The coordinates of B.
ii. The coordinates of C.
iii. The point identified by the coordinates (–3, –5).
iv. The point identified by the coordinates (2, – 4).
v. The abscissa of the point D.
vi. The ordinate of the point H.
vii. The coordinates of the point L.
viii. The coordinates of the point M
4. See Fig.3.14, and write the following.
i. The coordinates of B.
ii. The coordinates of C.
iii. The point identified by the coordinates (–3, –5).
iv. The point identified by the coordinates (2, – 4).
v. The abscissa of the point D.
vi. The ordinate of the point H.
vii. The coordinates of the point L.
viii. The coordinates of the point M
Explanation:
(i) According to figure, the coordinates of B are (−5, 2).
(ii) According to figure, the coordinates of C are (5, −5).
(iii) The point identified by the coordinates (−3, −5) in the figure is E.
(iv) The point identified by the coordinates (2, −4) in the figure is G.
(v) x coordinate of a point is called abscissa. Here, the abscissa of the point D is 6.
(vi) y coordinate of point is called is Ordinate. Here, the ordinate of the point H is -3.
(vii) According to figure, The coordinates of point L are (0, 5).
(viii) According to figure, The coordinates of point M are (−3, 0).
5. In which quadrant or on which axis do each of the points (– 2, 4), (3, – 1), (– 1, 0), (1, 2) and (– 3, – 5) lie? Verify your answer by locating them on the Cartesian plane.
5. In which quadrant or on which axis do each of the points (– 2, 4), (3, – 1), (– 1, 0), (1, 2) and (– 3, – 5) lie? Verify your answer by locating them on the Cartesian plane.
Explanation:
Point A (-2,4) lies is in 2nd Quadrant.
Point B (3,-1) lies in 4th Quadrant.
Point C (-1,0) lies on Negative x-axis.
Point D (1,2) lies in 1st Quadrant.
Point E (-3,-5) lies in 3rd Quadrant.
6.
Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.
6.
Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.
Explanation:
Let us assume the points to be plotted on the (x, y) are
A (-2, 8), B (-1, 7), C (0, -1.25), D (1, 3) and E (3, -1) from the table given above.
On the plane, mark the X-axis and the Y-axis. Mark the meeting point origin O.
Mark the names of quadrants and distances from origin.
Point A(-2,8) lies in 2nd Quadrant. Draw imaginary line starting 2 unit left of origin O and 8 units above of origin O. The meeting point of these two lines is the required point.
Point B(-1,7) lies in 2nd Quadrant. Draw imaginary line starting 1 unit left of origin O and 7 units above of origin O. The meeting point of these two lines is the required point.
Point C(0,-1.25) lies on y-axis, 1.25 units below the origin O. Draw imaginary line starting 1.25 units below of origin O and on the negative y- axis. The meeting point of these two lines is the required point.
Point D(1,3) lies in 1st Quadrant. Draw imaginary line starting 1 unit left of origin O and 3 units above of origin O. The meeting point of these two lines is the required point.
Point E(3,-1) lies in 4th Quadrant. Draw imaginary line starting 3 unit right of origin O and 1 units below of origin O. The meeting point of these two lines is the required point.
Also Read: Coordinate Geometry Class 9 Extra Questions
