Coordinate Geometry Test

Question 1
1 / -0

In the following figure, the area of the shaded region is _______.

A
23 sq. units

B
16 sq. units

C
10 sq. units

D
12 sq. units

Question 2
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The vertices of △MNO are O (4, -8), N (-2, 0) and M (4, 6), as shown in the figure. Find the area of △MNO.

A
22 square units

B
42 square units

C
62 square units

D
84 square units

Question 3
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A quadrilateral is given with the coordinates of its vertices in the figure below. Find its area.

A
116 square units

B
112 square units

C
108 square units

D
102 square units

Question 4
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Which of the given statements is true for the following points?

(2, 10), (4, 6), (-4, -22)

A
These are the vertices of an equilateral triangle.

B
These are non-collinear points.

C
These are the vertices of an isosceles triangle.

D
These are collinear points.

Question 5
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If points (x, 0), (0, y) and (2, 2) are collinear, then which of the following is true?

A
+ = 1

B
- = 1

C
+ = 1

D
+ = 2

Question 6
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Coordinates of points A, B and C are (2, 6), (4, 3) and (6, 6), respectively. What kind of a triangle is ΔABC?

A
Equilateral triangle

B
Isosceles triangle

C
Scalene triangle

D
Right-angled triangle

Question 7
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The three vertices of a parallelogram ABCD are A(1, -2), B(3, 6) and C(5, 10). The co-ordinates of the fourth vertex D are

A
(3, 2)

B
(2, 3)

C
(-3, 2)

D
(3, -2)

Question 8
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If the points (2a, a), (a, 2a) and (a, a) enclose a triangle of area 2 sq. units, then the value of a is

A
-2

B
4

C

D
2

Question 9
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What is the area of the triangle formed by joining the points (a, a + 2), (a + 2, a + 2) and (a - 2, a)?

A
2 sq. units

B
(2a - 2) sq. units

C
(2a + 2) sq. units

D
4a sq. units

Question 10
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The ratio in which the line segment joining points (3, -4) and (-5, 6) is divided by the y-axis is

A
3 : 5

B
5 : 2

C
2 : 1

D
3 : 1

Question 11
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Point A (2, p) lies in the first quadrant at a distance of 3 units from point (2, 2). Find the possible value of p.

A
5

B
3

C
2

D
1

Question 12
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What are the coordinates of the centroid of a triangle formed by joining points (2, 3), (3, 4) and (1, 2)?

A
(2, 3)

B
(3, 3)

C
(4, 3)

D
(5, 3)

Question 13
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A line segment joining the points (m, n) and (n, m) is divided in the ratio n : m internally by a point P. What will be the ordinate of this point P?

A

B
0

C

D
1

Question 14
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A triangle has a base of 12 units on the line 3x + 7y = 12. Find the area of the triangle if the third vertex is at (3, –5).

A
sq. units

B
226 sq. units

C
sq. units

D
225 sq. units

Question 15
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What are the coordinates of the third vertex of a triangle if the coordinates of its other two vertices are (-3, 2) and (2, -2), and its centroid lies at ?

A
(-1, -2)

B
(-1, -1)

C
(-1, 2)

D
(-1, -3)

Question 16
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A point moves 3 units to the east from the origin, then 5 units to the south, then 10 units to the west and finally 15 units to the north. In which quadrant will it lie?

A
1^st

B
2^nd

C
3^rd

D
4^th

Question 17
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The coordinates of the vertices of a rhombus PQRS are given in the figure below. Find the area of the rhombus.

A
84 square units

B
96 square units

C
48 square units

D
108 square units

Question 18
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Danial and Rena are both at origin facing in the positive y direction. If Danial moves 3 units to the right and two units upward, then what will be the distance between Danial and Rena?

A
units

B
units

C
units

D
units

Question 19
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A boy was in a park. He started walking from point (1, 5), reached point (5, 0), then moved to point (1, -5) and finally stopped at point (-3, 0). Find the area of the quadrilateral formed by joining these four points.

A
48 sq. units

B
40 sq. units

C
38 sq. units

D
49 sq. units

Question 20
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EFG is a triangle, where E is the vertex with coordinates (2, 1) and FG is the base with end coordinates (6, -2) and (8, 9). EH is an angle bisector, where H meets FG. What are the coordinates of H?

A
(,)

B
(,)

C
(,)

D
(7, 9)

Question 21

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Determine whether the given statements are true (T) or false (F) and choose the correct option accordingly:

(i) Point (-5, -4) and point (-3, -2) lie in the same quadrant.
(ii) A point lying on the x-axis at a distance of -4 units from the y-axis has coordinates (0, -4).
(iii) Abscissa of a point is negative in second quadrant as well as in third quadrant.
(iv) There are more points than one that lie on both the axes.

	(i)	(ii)	(iii)	(iv)
A	T	F	F	F
B	T	F	T	F
C	F	T	F	T
D	F	T	T	T

A

B

C

D

Question 22

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Fill in the blanks and choose the correct option accordingly:

(i) The abscissa and the ordinate of a point B lie 4 units to the left of the abscissa and one unit above the ordinate, respectively, of point A (3, -2). Point B lies in _____ quadrant.
(ii) The abscissa and the ordinate of a point lie 0.04 unit to the left of the abscissa and 0.04 unit below the ordinate, respectively, of point A (-10.96, 0.24). Point B lies in ____ quadrant.
(iii) The abscissa and the ordinate of a point lie 20 units to the right of the abscissa and 15 units below the ordinate, respectively, of point A (-15, 0). Coordinates of point B are ______.
(iv) Rohit moves 60 units towards east, then 30 units towards west and finally 10 units towards north. Considering his initial position to be origin, the coordinates of his final position must be ______.

	(i)	(ii)	(iii)	(iv)
A	III	II	(5, -15)	(30, 10)
B	IV	II	(5, 15)	(-20, 0)
C	III	IV	(-5, -10)	(0, 10)
D	II	III	(-5, -15)	(20, -10)

A

B

C

D

Question 23

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In the given figure, ACBD is a parallelogram with its diagonals AB and CD along the coordinate axes, AB = 18 units and CD = 14 units. Now, if S is a point which is 5 units to the right and 7 units below C, then find

(i) the sum of the abscissae of C, B and S
(ii) the sum of the ordinates of D, A and S

Choose the correct option from below:

A	(i) -9	(ii) 2
B	(i) -7	(ii) 2
C	(i) -8	(ii) 1
D	(i) -7	(ii) 1

A

B

C

D

Question 24

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In the given figure, ABC is an isosceles triangle, where altitude AO is drawn from origin O, length AO = 5a units and base BC = 6b units. Find the coordinates of all its vertices.

Choose the correct option from below:

P	A (0, 5a)	B (6b, 0)	C (0, -3b)
Q	A (0, 6b)	B (3b, 0)	C (-3b, 0)
R	A (0, 5a)	B (-3b, 0)	C (3b, 0)
S	A (5a, 0)	B (0, 3b)	C (0, 6b)

P

Q

R

S

Question 25

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Match the following:

Column I	Column II
(P) The area of rectangle OACB, with vertices O (0, 0), A (4, 0), B (0, 8) and C (4, 8), is	(i) 30 sq. units
(Q) The area of triangle ABC, with vertices A (0, 1), B (0, 13) and C (5, 5), is	(ii) 32 sq. units
(R) The area of triangle CAB, with vertices C (-5, 0), A (5, 0) and B (0, 8), is	(iii) 40 sq. units

Choose the correct match from below:

A	P - (iii)	Q - (ii)	R - (i)
B	P - (i)	Q - (iii)	R - (ii)
C	P - (ii)	Q - (iii)	R - (i)
D	P - (ii)	Q - (i)	R - (iii)

Coordinate Geom...

Question 1

23 sq. units

16 sq. units

10 sq. units

12 sq. units

Question 2

22 square units

42 square units

62 square units

84 square units

Question 3

116 square units

112 square units

108 square units

102 square units

Question 4

These are the vertices of an equilateral triangle.

These are non-collinear points.

These are the vertices of an isosceles triangle.

These are collinear points.

Question 5

+ = 1

- = 1

+ = 1

+ = 2

Question 6

Equilateral triangle

Isosceles triangle

Scalene triangle

Right-angled triangle

Question 7

(3, 2)

(2, 3)

(-3, 2)

(3, -2)

Question 8

-2

4

2

Question 9

2 sq. units

(2a - 2) sq. units

(2a + 2) sq. units

4a sq. units

Question 10

3 : 5

5 : 2

2 : 1

3 : 1

Question 11

5

3

2

1

Question 12

(2, 3)

(3, 3)

(4, 3)

(5, 3)

Question 13

0

1

Question 14

sq. units

226 sq. units

sq. units

225 sq. units

Question 15

(-1, -2)

(-1, -1)

(-1, 2)

(-1, -3)

Question 16

1st

2nd

3rd

4th

Question 17

84 square units

1^st

2^nd

3^rd

4^th