Coordinate Geometry Questions and Answers

Important Questions for Coordinate Geometry (Mathematics):

Q 1. If x is a positive integer such that the distance between points P(x, 2) and Q(3, –6) is 10 units, then x is equal to
A. 3
B. –3
C. –9
D. 9

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Answer:-D. 9

Q 2.  A line segment is of length 10 units. If the coordinates of its one end are (2, –3) and the abscissa of the other end is 10, then its ordinate is
A. 9, 6
B. -3, 9
C. 3, -9
D. 9, -6

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Answer:-C. 3, -9

Q 3. If the points (k, 2k), (3k, 3k) and (3, 1) are collinear, then k
A. -1/3
B. 1/3
C. 2/3
D. –2/3

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Answer:-A. -1/3

Q 4. The coordinates of the point on X-axis which are equidistant from the points (-3, 4) and (2, 5) are
A. (20, 0)
B. (-23, 0)
C. (4/5, 0)
D. none of these

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Answer:-D. none of these

Q 5.  If (–1, 2), (2, –1) and (3, 1) are any three vertices of a parallelogram, then
A. a = 2, b = 0
B. a = –2, b = 6
C. a = –2, b = 0
D. a = 6, b = 2

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Answer:-B. a = –2, b = 6

Q 6. The area of the triangle formed by (a, b + c), (b, c + a) and (c, a + b) is
A. a + b + c
B. abc
C. (a + b + c)²
D. 0

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Answer:-D. 0

Q 7. If (x, 2), (-3, -4) and (7, -5) are collinear, then x =
A. 60
B. 63
C. –63
D. –60

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Answer:-C. –63

Q 8.  If points (t, 2t), (–2, 6) and (3, 1) are collinear, then t =
A. ¾
B. 4/3
C. 5/3
D. 3/5

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Answer:-B. 4/3

Q 9. If the area of the triangle formed by the points (x, 2x), (–2, 6) and (3, 1) is 5 square units, then x =
A. 2/3
B. 3/5
C. 3
D. 5

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Answer:-A. 2/3

Q 10. If the centroid of a triangle  is (1, 4) and two of its vertices are (4, –3) and (–9, 7), then the area of the triangle is
A. 183 sq. units
B. 183/2 sq. units
C. 366 sq. units
D. 183/4 sq. units

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Answer:-B. 183/2 sq. units

Q 11. The line segment joining points (–3, –4), and (1, –2) is divided by y-axis in the ratio
A. 1 : 3
B. 2 : 3
C. 3 : 1
D. 2 : 3

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Answer:-C. 3 : 1

Q 12. The ratio in which (4, 5) divides the join of (2, 3) and (7, 8) is
A. 2 : 3
B. –3, 2
C. 3 : 2
D. -2 : 3

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Answer:-A. 2 : 3

Q 13. The ratio in which the x-axis divides the segment joining (3, 6) and (12, -3) is
A. 2 : 1
B. 1 : 2
C. –2 : 1
D.  1 : –2

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Answer:-A. 2 : 1

Q 14. If the centroid of the triangle formed by the points (a, b) (b, c) and (c, a) is at the origin, then
a³ + b³ + c³ =
A. abc
B. 0
C. a + b + c
D. 3 abc

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Answer:-D. 3 abc

Q 15. If the points (1, 2), (–5, 6) and (a, –2) are collinear, then a =
A. –3
B. 7
C. 2
D. –2

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Answer:-B. 7

Q 16. If the centroid of the triangle formed by (7, x), (y, –6) and (9, 10) is at (6, 3), then (x, y) =
A. (4, 5)
B. (5, 2)
C. (–5, –2)
D. (5, 4)

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Answer:-B. (5, 2)