Coordinate Geometry

Point (–3, 5) lies in the
A. first quadrant

B. second quadrant

C. third quadrant

D. fourth quadrant

Signs of the abscissa and ordinate of a point in the second quadrant are respectively
A. +, +

B. –, –

C. –, +

D. +, –

Point (0, –7) lies
A. on the x –axis

B. in the second quadrant

C. on the y-axis

D. in the fourth quadrant

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

Abscissa of all the points on the x-axis is
A. 0

B. 1

C. 2

D. any number

Ordinate of all points on the x-axis is
A. 0

B. 1

C. – 1

D. any number

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

B. ordinate

C. origin

D. quadrant

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

B. II quadrant

C. III quadrant

D. IV quadrant

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

If 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

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

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 x-axis, then the point P has
A. x – coordinate = – 5

B. y - coordinate = 5 only

C. y – coordinate = – 5 only

D. y – coordinate = 5 or –5

On plotting the points O (0, 0), A (3, 0), B (3, 4), 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

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 RC. Only S

D. P and R

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

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

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

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

In Fig. 3.1, coordinates of P are


A. (– 4, 2)

B. (–2, 4)

C. (4, – 2)

D. (2, – 4)

In Fig. 3.2, the point identified by the coordinates (–5, 3) is


A. T

B. R

C. L

D. S

The point whose ordinate is 4 and which lies on y-axis is
A. (4, 0)

B. (0, 4)

C. (1, 4)

D. (4, 2)

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

The point which lies on y–axis at a distance of 5 units in the negative direction of y–axis is
A. (0, 5)

B. (5, 0)

C. (0, – 5)

D. (– 5, 0)

The perpendicular distance of the point P (3, 4) from the y-axis is
A. 3

B. 4

C. 5

D. 7

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

Point (3, 0) lies in the first quadrant.

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

Points (1, –1) and (–1, 1) lie in the same quadrant.

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

The coordinates of a point whose ordinate is and abscissa is 1 are .

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

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

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

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

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

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)

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

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)

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

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 the points L and M?

In which quadrant or on which axis each of the following points lie?

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

Which of the following points lie on 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)

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

Use scale 1 cm = 0.25 units

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 y-axis at a distance of –7 units from x-axis?

Find the coordinates of the point

(i) which lies on x and y axes both.

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

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

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)

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

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

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.

From the 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.

Plot the 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 the points A and B.

(ii) Extend this line segment and write the coordinates of a point on this line which lies outside the line segment AB.