CHAPTER-3, COORDINATE GEOMETRY - Extra Questions

1. Point (–3, 5) lies in the 

(A) first quadrant (B) second quadrant 

(C) third quadrant (D) fourth quadrant

Explanation: 

Every point in the second quadrant has a positive ordinate and a negative abscissa, as we are aware.

In point (-3, 5), -3 is a negative number.

Positive is ordinate, or five.

In the second quadrant, it is located.

The point is located in the second quadrant as a result.

2. Signs of the abscissa and ordinate of a point in the second quadrant are respectively 

(A) +, + (B) –, – (C) –, + (D) +, –

Explanation: 

The correct selection is A Positive, Negative

The sign convention for a coordinate plane in various quadrants is depicted in the diagram below.

This reveals that the ordinate sign and abscissa of a point in the second quadrant are, respectively, positive and negative.n

3. Point (0, –7) lies 

(A) on the x –axis (B) in the second quadrant 

(C) on the y-axis (D) in the fourth quadrant

Explanation: 

A point's distance from the y-axis is measured by its abscissa, or x-coordinate, and its distance from the x-axis, or y-coordinate.

The point whose ordinate is y and whose ordinate abscissa is x is said to have coordinates of (x, y).

As a result, the y-axis is defined by the point (0, -7).

4. Point (– 10, 0) lies 

(A) on the negative direction of the x-axis 

(B) on the negative direction of the y-axis 

(C) in the third quadrant 

(D) in the fourth quadrant

Explanation: 

We are aware that ordinate and abscissa are used to express a point's location on a graph.

The x-axis's coordinates are known as the abscissa.

The distance from the y-axis, as measured along the x-axis,

The abscissa in the point (-10,0) is negative.

As a result, it is located on the x-axis's negative side.

As a result, the point is located along the x-axis' negative direction.

5. Abscissa of all the points on the x-axis is 

(A) 0 (B) 1 (C) 2 (D) any number

Explanation: 

We are aware that ordinate and abscissa are used to express a point's location on a graph.

The x-axis's coordinates are known as the abscissa.

The distance from the y-axis, as measured along the x-axis,

The abscissa is the distance between a point and the y-axis, scaled with the x-axis.

1. The ordinate is the distance a point is from the x-axis scaled with the y-axis.

2. Coordinate is the combination of the terms abscissa and ordinate.

The abscissa of any point on the x-axis is therefore any number.

6. Ordinate of all points on the x-axis is (A) 0 (B) 1 (C) – 1 (D) any number

Explanation: 

We are aware that the x-axis coordinates are (x, 0).

Any point on the x-axis has coordinates of (x, 0), where x is the abscissa and 0 is the ordinate.

As a result, all points on the x-axis have an ordinate of 0.

7. The point at which the two coordinate axes meet is called the 

(A) abscissa (B) ordinate (C) origin (D) quadrant 

Explanation: 

The origin is the place where the coordinate axes meet, which is option C. In the image above, O stands in for the point.

8. A point both of whose coordinates are negative will lie in 

(A) I quadrant (B) II quadrant (C) III quadrant (D) IV quadrant

Explanation: 

The response is C.

Because the third quadrant's x- and y-coordinates are negative, a point with both negative coordinates will be located there.

9. Points (1, – 1), (2, – 2), (4, – 5), (– 3, – 4) 

(A) lie in II quadrant (B) lie in III quadrant (C) lie in IV quadrant (D) do not lie in the same quadrant

Explanation: 

The solution is D.

The x-coordinate is positive while the y-coordinate is negative in the points (1-1), (2-2), and (4-5) respectively.

They are all located in Quadrant IV.

Both the x and y coordinates at points (-3, -4) are negative. It is located in the III quadrant.

Since they are not in the same quadrant, the supplied points.

10. If the y coordinate of a point is zero, then this point always lies 

(A) in I quadrant (B) in II quadrant (C) on x - axis (D) on y - axis

Explanation: 

C) Given, the y-coordinate is zero is the appropriate choice.

The ordinate is 0, while the abscissa can be any value x.

The point at which x can take any value, either positive or negative, is (x,0).

On the x-axis, the point (x,0) is located.

As a result, choice C is accurate.


11. The points (–5, 2) and (2, – 5) lie in the 

(A) same quadrant (B) II and III quadrants, respectively 

(C) II and IV quadrants, respectively (D) IV and II quadrants, respectively

Explanation: 

The response is C.

The x-coordinate is negative and the y-coordinate is positive at the position (-5, 2).

As a result, it is located in the II quadrant. Point (2, -5) is in the IV quadrant since the x-coordinate is positive and the y-coordinate is negative.

12. If the perpendicular distance of a point P from the x-axis is 5 units and the foot of 

the perpendicular lies on the negative direction of the x-axis, then point P has 

(A) x coordinate = – 5 (B) y coordinate = 5 only 

(C) y coordinate = – 5 only (D) y coordinate = 5 or –5

Explanation: 

The fact that

Its separation from the x-axis is indicated by the ordinate or y-coordinate.

It follows that

A point P's ordinate, or the distance perpendicular to the x-axis, is equal to five units.

The x-axis's negative orientation does not determine the sign of the ordinate.

As a result, P has a y coordinate of 5 or -5.

13. On plotting the points O (0, 0), A (3, 0), B (3, 4), and C (0, 4) and joining OA, AB, BC and CO which of the following figure is obtained? (A) Square (B) Rectangle (C) Trapezium (D) Rhombus

Explanation: 

The right response is A Rectangle.

The origin in this case is at O(0,0), while A(3,0) is located along the x-axis' positive direction. B(3,4) is located in the first quadrant, while C(0,4) lines up with the positive y-axis direction. A rectangle is a result of uniting the triangles OA, AB, BC, and CO.

14. If P (– 1, 1), Q (3, – 4), R(1, –1), S(–2, –3) and T (– 4, 4) are plotted on the graph paper, then the point(s) in the fourth quadrant are (A) P and T (B) Q and R (C) Only S (D) P and R

Explanation: 

The response is B.

Point P(-1, 1) is located in the lI quadrant since its x- and y-coordinates are both one unit.

The points Q(3, - 4), R(1, - 1), S(-2, -3), and R(-4, -4) can all be plotted in a similar way.

The graph clearly shows that points R and Q are located in the fourth quadrant.

15. If the coordinates of the two points are P (–2, 3) and Q(–3, 5), then (abscissa of P) – (abscissa of Q) is (A) – 5 (B) 1 (C) – 1 (D) – 2

Explanation: 

The two supplied coordinates are P (-2, 3), and Q (-3, 5).

We are aware that P's abscissa is equal to -2.

Q's abscissa is equal to -3.

The (abscissa of P) - (abscissa of Q) must be located.

The values (abscissa of P) - (abscissa of Q) = -2 - (-3)

= -2 + 3

= 1 are substituted.

Since (abscissa of P) - (abscissa of Q) is 1, the answer is 1.

16. If P (5, 1), Q (8, 0), R (0, 4), S (0, 5) and O (0, 0) are plotted on the graph paper, then the point(s) on the x-axis are (A) P and R (B) R and S (C) Only Q (D) Q and O

Explanation: 

The solution is D.

We are aware that a point is on the x-axis. if its zero y-coordinate.

Q and O are found to be on the x-axis when the given points are plotted on graph paper.

17. Abscissa of a point is positive in (A) I and II quadrants (B) I and IV quadrants (C) I quadrant only (D) II quadrant only

Explanation: 

The response is B.

A point's abscissa is positive in the I and IV quadrants.

18. The points whose abscissa and ordinate have different signs will lie in 

(A) I and II quadrants (B) II and III quadrants (C) I and III quadrants (D) II and IV quadrants

Explanation: 

The solution is D.

The (-x,y) or (x, -y) points that have differing abscissa and ordinate signs will be located in the II and IV quadrants.

19. In Fig. 3.1, coordinates of P are 

(A) (– 4, 2) (B) (–2, 4) (C) (4, – 2) (D) (2, – 4)

Explanation: 

The right answer is B) Because the provided point P is in the second quadrant, its abscissa will be negative, and it's ordinate positive. Additionally, P's y-coordinate is 4, its perpendicular distance from the X-axis is 4, and its perpendicular distance from the Y-axis is 2. Thus, the coordinate of x is -2. P's coordinates are (-2,4) as a result. 

As a result, (B) is the right response.

20. In Fig. 3.2, the point identified by the coordinates (–5, 3) is (A) T (B) R (C) L (D) S

Explanation: 

The fourth quadrant is where point T is located, hence choice A is the correct one. T is 3 units away from the y-axis and 5 units away from the x-axis below the x-axis. Therefore, T is the point designated by the coordinates (-5,3).

21. The point whose ordinate is 4 and which lies on the y-axis is (A) (4, 0) (B) (0, 4) (C) (1, 4) (D) (4, 2)

Explanation: 

The right answer is B (0,4).

The y-axis point's abscissa is zero.

So, (0, 4) is the point that has the ordinate 4 and is on the y-axis.

22. Which of the points P(0, 3), Q(1, 0), R(0, – 1), S(–5, 0), T(1, 2) do not lie on the x-axis? 

(A) P and R only (B) Q and S only (C) P, R and T (D) Q, S and T

Explanation: 

The response is C.

We are aware that a point will lie on the x-axis if its coordinates are of the type (x,0), which means that its y-coordinate is zero.

Points P(0, 3), R(0, -1), and T(1, 2) in this case do not lie on the x-axis since their y-coordinates are not zero.

23. The point which lies on the y-axis at a distance of 5 units in the negative direction of the y-axis is 

(A) (0, 5) (B) (5, 0) (C) (0, – 5) (D) (– 5, 0)

Explanation: 

The right response is C (0,-5)

It is evident that the point's x-coordinate is zero because it is on the y-axis. The point's y-coordinate is negative since it is located 5 units away in the opposite direction of the y-axis. Therefore, the necessary point is (0, -5).

24. The perpendicular distance of the point P (3, 4) from the y-axis is (A) 3 (B) 4 (C) 5 (D) 7

Explanation: 

The right response is A 3 units.

The abscissa of the point is the perpendicular distance of the point from the Y-axis measured along the X-axis. So, three units are the solution.

25. Write whether the following statements are True or False? Justify your answer. 

(i) Point (3, 0) lies in the first quadrant. (ii) Points (1, –1) and (–1, 1) lie in the same quadrant. 

(iii) The coordinates of a point whose ordinate is  -½  and abscissa is 1 are -½,1

(iv) A point lies on the y-axis at a distance of 2 units from the x-axis. Its coordinates are (2, 0). 

(v) (–1, 7) is a point in the II quadrant.

Explanation: 

The fact that

On the y-axis are the locations with 0 as their x-coordinate.

On the x-axis are the spots with 0 as the y-coordinate.

A point's distance from the y-axis is measured by its abscissa, or x-coordinate, and its distance from the x-axis, or y-coordinate.

The provided point is (3, 0).

Here, the ordinate is 0, therefore the point is on the x-axis.

The claim is untrue as a result.

26. Write the coordinates of each of the points P, Q, R, S, T, and O from Fig. 3.5.

Explanation: 

The following are the coordinates for the points P, Q, R, S, T, and O:

P = (1, 1)

Q = (-3, 0)

R = (-2.-3)

S = (2,1)

T = (4,-2)

O = (0,0)

27. Plot the following points and write the name of the figure obtained by joining them in order: P(– 3, 2), Q (– 7, – 3), R (6, – 3), S (2, 2)

Explanation: 

Mark a point on the coordinate axes, X' OX and Y' OY. Points P(-3, 2), Q(-7, -3), R(6,-3), and S(2, 2) are located in the II quadrant, III quadrant, IV quadrant, and I quadrant, respectively. Trapezium PQRS is the result of plotting the points on graph paper.


28. Plot the points (x, y) given by the following table: 

x 2 4 – 3 – 2 3 0 y 4205 – 3 0

Explanation: 

The graph's points P(2, 4), Q(4, 2), R(-3, 0), S(-2, 5), T(3, -3), and O(0, 0) are obtained by plotting the provided points on it.

29. Plot the following points and check whether they are collinear or not : 

(i) (1, 3), (– 1, – 1), (– 2, – 3) 

(ii) (1, 1), (2, – 3), (– 1, – 2) 

(iii) (0, 0), (2, 2), (5, 5)

Explanation: 

Points along a line.

Collinear points are those that are situated along a single or shared straight line.

On the graph, which is displayed below, the supplied points (0,0), (2,2), and (5,5) are drawn.


It can be seen from the graph that every one of the given points lies in a straight line.

The specified points are therefore collinear.

30. Without plotting the points indicate the quadrant in which they will lie, if 

(i) ordinate is 5 and abscissa is – 3 

(ii) abscissa is – 5 and ordinate is – 3 

(iii) abscissa is – 5 and ordinate is 3 

(iv) ordinate is 5 and abscissa is 3

Explanation: 

(i) The point (-3,5) is in the second quadrant since the ordinate is positive and the abscissa is negative.

(ii) The ordinate and abscissa at points (-5, -3) are both negative, placing them in the third quadrant.

(iii) The point (-5,3) is in the second quadrant since the ordinate is positive and the abscissa is negative.

(iv) The ordinate and abscissa at point (3,5) are both positive, placing them in the first quadrant.

31. In Fig. 3.6, LM is a line parallel to the y-axis at a distance of 3 units. 

(i) What are the coordinates of the points P, R and Q? 

(ii) What is the difference between the abscissa of points L and M? 

Explanation: 

Given that LM is a line perpendicular to the y-axis, its distance from the y-axis perpendicular to it is 3 units.

a. The coordinates of the point P, which are (3, 2) [because it is perpendicular to the X-axis and is 2]

Point Q's coordinates are (3, -1) because its perpendicular distance from the X-axis is 1 in the direction opposite to the Y-axis.

Point R's coordinates are (3, 0), which indicates that it is on the X-axis and has a zero y-coordinate.

b. Abscissa of point L equals 3, while that of point M equals 3.

Difference: 3 - 3 equals 0.

32. In which quadrant or on which axis do each of the following points lies? 

(– 3, 5), (4, – 1), (2, 0), (2, 2), (– 3, – 6)

Explanation: 

A. The x-coordinate at location (-3, 5) is negative while the y-coordinate is positive. It's located in quadrant II.

b. The x-coordinate is positive and the y-coordinate is negative at point (4, -1). It's located in sector IV.

c. The x and y coordinates at location (2, 0) are both positive. Thus, it is X-axis-aligned.

d. The x-coordinate and y-coordinate at points (2, 2) are both positive. It is located in the I quadrant.

e. The x- and y-coordinates at position (-3, -6) are both negative. It is located in the III quadrant.

33. Which of the following points lie on the y-axis? A (1, 1), B (1, 0), C (0, 1), D (0, 0), E (0, – 1), F (– 1, 0), G (0, 5), H (– 7, 0), I (3, 3).

Explanation : 

If a point's x-coordinate is zero, then we know it is on the Y-axis.

The x-coordinates of the following locations are zero: C(0,1), D(0,0), E(0,-1) and G(0,5).

These locations are thus on the Y-axis.

Additionally, since D(0, 0) is the intersection of the two axes, we can assume that it is located both on the x- and y-axes.

34. Plot the points (x, y) given by the following table. Use scale 1 cm = 0.25 units 

 x 1.25 0.25 1.5 – 1.75 

 y – 0.5 1 1.5 – 0.25

Explanation: 

Assume that the coordinate axes are X'OX and Y'OY.

Plot the following points on the graph paper: 1.25, -0.5, 0.25, 1, 1.5, and 1.75, -0.25.

The coordinates P (1.25, -0.5), Q (0.25, 1), R (1.5, 1.5), and S(-1.75, -0.25) are obtained after charting.

35. A point lies on the x-axis at a distance of 7 units from the y-axis. What are its coordinates? What will be the coordinates if it lies on the y-axis at a distance of –7 units from the x-axis?

Explanation: 

Given that, the point is in the x-axis's positive direction. As a result, its y-coordinate will be zero and it will be 7 units away from the Y-axis.

Its location is therefore (7, 0).

If it lies in the negative direction of the y-axis, then its x-coordinate will be zero and its distance from the x-axis is 7 units, therefore its coordinates are (0, -7).

36. Find the coordinates of point (i) which lies on x and y axes both. 

(ii) whose ordinate is – 4 and which lies on the y-axis. 

(iii) whose abscissa is 5 and which lies on the x-axis.

Explanation: 

a. The origin, with coordinates of (0, 0), is the point that lies on both the x and y axes.

b. The point (0, -4) has an ordinate of -4 and is on the y-axis, meaning that its x-coordinate is zero.

c. The point (5, 0) has a y-coordinate of zero, an abscissa of 5, and is located on the x-axis.

37. Taking 0.5 cm as 1 unit, plot the following points on the graph paper : 

A (1, 3), B (– 3, – 1), C (1, – 4), D (– 2, 3), E (0, – 8), F (1, 0)

Explanation: 

Point A(1, 3) is in the I quadrant since its x and y values are both positive.

Point B(-3, -1) is in the III quadrant since its x and y coordinates are both negative.

The x and y coordinates are positive and negative, respectively, at point C(1, -4). This places it in sector IV.

Point D(-2, 3) is in the II quadrant since its x-coordinate is negative and its y-coordinate is positive.

The x-coordinate at point E(0, -8) is zero, so it is on the y-axis, while the y-coordinate at point F(1, 0) is zero, so it is on the x-axis.

The following graph is produced by plotting the provided points.

38. Points A (5, 3), B (– 2, 3) and D (5, – 4) are three vertices of a square ABCD. Plot these points on graph paper and hence find the coordinates of the vertex C.

Explanation: 

Consider point C on the graph where ABCD is a square, meaning that all of its sides (AB, BC, CD, and AD) are equal. 

Therefore, the ordinate of C should be equal to the ordinate of D, which is 4, and the abscissa of C should be equal to the abscissa of B, which is 2. As a result, C's coordinates are (2, -4).

Below is a graph that was created by graphing points A, B, C, and D. 

39. Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units respectively, with one vertex at the origin, the longer side lying on the x-axis and one of the vertices lying in the third quadrant.

Explanation: 

Let's say the rectangle is OABC, with O as the origin for the vertex.

Make OA the lengthier side.

∴ O has the coordinates O(0,0). 

The coordinate of A is A(5,0) because one of the vertexes is in the third quadrant and the longer side of length 5 units lie on the x-axis. 

The rectangle is located in the III quadrant as well.

∴ On the y-axis, the side OC will be located in the negative direction.

Then, OC has a length of 3 units.

∴ C will have the coordinates C(0,3). 

The coordinates of B will then obviously be (5, 3).

In this instance, OCIIAB and <AOC=90o, so is a rectangle.

The rectangle's vertices are O(0,0), A(5,0), B(5,3), and C(0,3).

40. Plot the points P (1, 0), Q (4, 0) and S (1, 3). Find the coordinates of the point R such that PQRS is a square.

Explanation: 

PQRS is a square, so there.

P, Q, and S are located at (1, 0), (4, 0), and (1, 3), respectively.

The location of R's coordinates must be ascertained.

Think about the coordinates P(1, 0).

A positive x-coordinate and a zero y-coordinate are present.

As a result, point P is located on the x-axis.

Think about the coordinates Q(4, 0).

A positive x-coordinate and a zero y-coordinate are present.

As a result, point Q is located on the x-axis.

Taking into account S(1, 3)

The x-coordinate and y-coordinate are both positive.

As a result, S is located in the first quadrant.

Plotting the points P, Q, and S at this time

41. From Fig. 3.8, answer the following : (i) Write the points whose abscissa is 0. 

(ii) Write the points whose ordinate is 0. (iii) Write the points whose abscissa is – 5.

Explanation: 

Solution (i) We are aware that the 0 abscissa point will be located on the y-axis. Therefore, A, L, and O are the necessary points whose abscissa is 0.

(ii) We are aware that the 0 ordinate points will be on the x-axis. Therefore, G, I, and O are the necessary locations whose ordinate is 0.

(iii) Abscissa -5 is negative in this instance, indicating that the point will be in the II and III quadrants. D and H are therefore the necessary points, and their abscissa is -5.

42. Plot points A (1, – 1) and B (4, 5) (i) Draw a line segment joining these points. Write the coordinates of a point on this line segment between points A and B.(ii) Extend this line segment and write the coordinates of a point on this line that lies outside the line segment AB.

Explanation: 

Point A(1, -1) is in the IV quadrant since its x-coordinate is positive and its y-coordinate is negative.

Point B(4, 5) is in the I quadrant since both of its coordinates are positive. We obtain the following graph by plotting these points.


(i) The line segment AB is created by connecting the points A and B. Draw a line perpendicular to the X-axis starting at x = 2 in order to determine the coordinates of a point on this line segment between A and B. Say that line segment AB meets it at P [because x = 2 is between A and B]. Draw an angle from P that is perpendicular to the Y-axis and intersects it at y = 1. As a result, we obtain the points (2, 1) that lie on the AB line segment.

Extend the line segment AB in (ii). Draw an extended line segment at Q on the Y-axis at y = - 3 and state it is perpendicular to the X-axis from x = 0. As a result, we are left with the point Q(0, -3) which is outside of the AB line segment.

CHAPTER-3, COORDINATE GEOMETRY