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CBSE Class 10  >  Class 10 Test  >  Olympiad Preparation  >  Math Olympiad Test: Coordinate Geometry- 2 - Class 10 MCQ

Math Olympiad Test: Coordinate Geometry- 2 - Free MCQ with solutions


MCQ Practice Test & Solutions: Math Olympiad Test: Coordinate Geometry- 2 (15 Questions)

You can prepare effectively for Class 10 Olympiad Preparation for Class 10 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Math Olympiad Test: Coordinate Geometry- 2". These 15 questions have been designed by the experts with the latest curriculum of Class 10 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 15 minutes
  • - Number of Questions: 15

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Math Olympiad Test: Coordinate Geometry- 2 - Question 1
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Find the third vertex of a ΔABC if two of its vertices are B (-3, 1), C (0, -2), and its centroid is at the origin.

Detailed Solution: Question 1

B  (-3, 1) C (0, -2)
Let the third vertex be A (x, y)
G = (0, 0)
= 0 ⇒ x = 3 and 
⇒ y - 1 = 0 ⇒ y = 1
A (3, 1)

Math Olympiad Test: Coordinate Geometry- 2 - Question 2
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The circumcentre of a triangle is (3, 3). If its two vertices are (4, 6) and (0, 4) find the third vertex of the triangle.

Detailed Solution: Question 2

Let P (3, 3) be the circumcentre of ΔABC, C(x, y) be the third vertex

PA = PB = PC
PA2 = PB2 = PC2
PA2 = PC2
⇒ (4 - 3)2 + (6 - 3)2
= (x - 3)2 + (y - 3)2
⇒ 1 + 9 = x2 + 9 - 6x + y2 + 9 - 6y
⇒ x2 + y2 - 6x - 6y + 8 = 0 ...(1)
and PB2 = PC2
⇒ (0 - 3)2 + (4, -3)2 = (x - 3)2 + (y - 3)2
⇒ 9 + 1 = x2 + 9 - 6x + y2 - 6y + 9
Equations (1) and (2) are identical
(x - 3)2 + (y - 3 )2 = 10
So, (6, 2) is the required point.

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Math Olympiad Test: Coordinate Geometry- 2 - Question 3
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In which ratio does the point P (1, 2) divides the join of A (-2, 1) and B (7, 4)?

Detailed Solution: Question 3


Let the ratio be k : 1

⇒ 6k = 3
⇒ k = 3/6 = 1/2

Math Olympiad Test: Coordinate Geometry- 2 - Question 4
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If (2, -2), (-2, 1) and (5, 2) are vertices of a right angled triangle, then the area of triangle is

Detailed Solution: Question 4

Area of triangle 
= 1/2 [x1 (y2 - y3) + x2 (y3 -y1) + x3 (y1 - y2) 
= 1/2 [2 (1 − 2) + (−2) (2 + 2) + 5 (−2 −1)]
= 1/2 [−2−8 −15] = 25/2 = 12.5 sq. units

Math Olympiad Test: Coordinate Geometry- 2 - Question 5
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The centre of a circle is (4, 5) A(8, 10) is a point on the circumference. Find the other end of diameter of the circle through A.

Detailed Solution: Question 5

Let the other end be (x, y)

Math Olympiad Test: Coordinate Geometry- 2 - Question 6
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The ends of a diameter of a circle have the coordinates (4, 3) and (-4, -3), PQ is another diameter where P has co-ordinate 
 
find the coordinates of Q.

Detailed Solution: Question 6

Mid-point of (4, 3) and (-4, -3)

Math Olympiad Test: Coordinate Geometry- 2 - Question 7
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The vertices of a triangle are A(1, 1), B(-2, -5) and C(2, 2) find the length of the medium through C.

Detailed Solution: Question 7


Math Olympiad Test: Coordinate Geometry- 2 - Question 8
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What is the circumradius of the triangle whose vertices are (2, -2), (8, 6), and (8, -2)?

Detailed Solution: Question 8


Let P(x, y) be the circumcentre
PA = PB = PC
⇒ PA2 = PB2
⇒ (x - 2)2 + (y + 2)2
= (x - 8)2 + (y - 6)2
⇒ x2 + 4 - 4x + y2 + 4 - 4y
= x2+ 64 - 16x + y2 + 36 - 12y
⇒ - 4x + 16x + 4y + 12y = 100 - 8
⇒ 12x + 16y = 92 ⇒ 3x+ 4y = 23 ...(1)
and PB2 = PC2
⇒ (x - 8)2 + (y - 6)2 = (x - 8)2 + (y + 2)2
⇒ y2 + 36 - 12y = y2 + 4 + 4y
⇒ 16y = 32 ⇒ y = 2
3x = 23 - 4 ⇒ 2 = 15 ⇒ x = 5
P (5, 2)
∴ PA

Math Olympiad Test: Coordinate Geometry- 2 - Question 9
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The sum of the square of the distance of a moving point from two fixed points (a, 0) and (-a, 0) is equal to the constant quantity 2c2. Find the equation of its locus.

Detailed Solution: Question 9


Here (x -a)2 + (y - 0)2 = 2c2
x2 + a2 - 2ax + y2 = 2c2
and (x + a)2 + (y - 0)2 = 2c2
⇒ x2 + a2 + 2ax + y2 + 2c2
Now x2 + a2 - 2ax + y2 = x2 + a2 + 2ax + y2
⇒ 4ax = 0 ⇒ x = 0 or a = 0
(x - 0)2 + y2 = 2c2
⇒ x0 + y2 = 2c2

Math Olympiad Test: Coordinate Geometry- 2 - Question 10
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What is the distance of the point (4, 7) from the y-axis?

Detailed Solution: Question 10

Distance of the point (4, 7) from (0, y)
= x co-ordinate
= 4

Math Olympiad Test: Coordinate Geometry- 2 - Question 11
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If the distance between the points (3, 0) and (0, y) is 5 units. y is positive then what is value of y?

Detailed Solution: Question 11

(3 - 0)2 + (0 - y)2 = 52
9 + y2 = 25 ⇒ y2 = 16 ⇒ y = ± 4
y is positive, ∴ y = 4

Math Olympiad Test: Coordinate Geometry- 2 - Question 12
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If the centroid of the triangle is formed by points P(a, b), Q(b, c) and R(c, a) is at the origin. What is the value of a + b +c?

Detailed Solution: Question 12

Math Olympiad Test: Coordinate Geometry- 2 - Question 13
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If the point P(-1, 2) divides externally the line segment joining A(2, 5) and B in the ratio 3 : 4. What is the co-ordinate of point B?

Detailed Solution: Question 13

Math Olympiad Test: Coordinate Geometry- 2 - Question 14
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The points A(3, 1), B(0, 4), C(-3, 1), D(0, -2) are vertices of a

Detailed Solution: Question 14

The given points are A (0,-2), B(3,1), C(0,4) and D(-3,1)

Thus, diagonal PR = diagonal QS 
Therefore, the given points from a square. 

Math Olympiad Test: Coordinate Geometry- 2 - Question 15
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If the point (x, 4) lies on a circle whose center is at the origin and radius is 5, What is the value of x?

Detailed Solution: Question 15


OP = 5
⇒ OP2 = 25
⇒ (x - 0)2 + (4 - 0)2 = 25
⇒ x2 + 16 = 25
⇒ x2 = 9 ⇒ x = ± 3

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This test contains 15 MCQs on Math Olympiad Test: Coordinate Geometry- 2 with detailed solutions for each question. It is part of the Olympiad Preparation for Class 10 course on EduRev, designed to align with the current Class 10 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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