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CBSE Class 10  >  Class 10 Test  >  Olympiad Preparation  >  Math Olympiad Test: Coordinate Geometry- 1 - Class 10 MCQ

Math Olympiad Test: Coordinate Geometry- 1 - Free MCQ with solutions


MCQ Practice Test & Solutions: Math Olympiad Test: Coordinate Geometry- 1 (10 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- 1". These 10 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: 10 minutes
  • - Number of Questions: 10

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Math Olympiad Test: Coordinate Geometry- 1 - Question 1
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Find the value of k for which the points A (3, 2), B (4, k) and C (5, 3) are collinear.

Detailed Solution: Question 1

The points A (3, 2), B (4, K), and C (5, 3) are collinear then area (ΔABC) = 0
⇒ 1/2 [3(k − 3)+ 4(3 − 2) + 5(2 − k)] = 0
⇒ 3k - 9 + 4 + 10 - 5k = 0
⇒ -2k + 5 = 0 ⇒ k = 5/2

Math Olympiad Test: Coordinate Geometry- 1 - Question 2
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Find ratio in which the line 2x + y - 4 = 0 divides the line segment joining A(2, -2) and B(3, 7).

Detailed Solution: Question 2


Let the point P (x, y) divide the line AB in the ratio k : 1

This point P(x, y) lies on the line
2x + y - 4 = 0

⇒ 6k + 4+ 7k - 2 - 4k - 4 = 0
⇒ 9k - 2 = 0 ⇒ 9k = 2
⇒ k = 2/9 = 2 : 9

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Math Olympiad Test: Coordinate Geometry- 1 - Question 3
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The co-ordinates of ends of a diameter of a circle are (4, -1) and (-2, -5). Find the centre of the circle.

Detailed Solution: Question 3

Ends of diameter of circle are (4, -1) and (-2, -5)
centre = Mid-point of (4, -1) and (-2, -5)

Math Olympiad Test: Coordinate Geometry- 1 - Question 4
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The area of a triangle with vertices (a, b + c) and (b, c + a) and (c, b + a) is

Detailed Solution: Question 4

Area of triangle
= 1/2 [a(c + a - a - b) + b (a + b - b - c) + c (b + c - c - a)]
= 1/2 [a(c − b)+ b(a − c) + c(b − a)]
= 1/2 [ac − ab + ab − bc + bc − ac]
= 1/2 × 0 = 0

Math Olympiad Test: Coordinate Geometry- 1 - Question 5
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Find the co-ordinates of the points which trisects the line joining (-3, 5) and (6, -7).

Detailed Solution: Question 5

Let P(x, y) be the point

Math Olympiad Test: Coordinate Geometry- 1 - Question 6
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The ends of a diagonal of a square have the coordinates (a, 1) and (-1, a), find a if the area of the square is 50 square units.

Detailed Solution: Question 6


Let side of the square be x.
x2 + x2 = (-1 - a)2 + (a - 1)2
⇒ 2x2 = 1 + a2 + 2a + a2 + 1 - 2a
⇒ x2 = a2 + 1
⇒ 50 = a2 + 1 ⇒ a2 = 49
⇒ a = ±7

Math Olympiad Test: Coordinate Geometry- 1 - Question 7
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Two vertices of a triangle are (2, -4) and (1, 3). If the origin is the centroid of the triangle then what is the third vertex?

Detailed Solution: Question 7


third vertex = (-3, 1)

Math Olympiad Test: Coordinate Geometry- 1 - Question 8
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What is the locus of a point equidistant from the point (2, 4) and y-axis?

Detailed Solution: Question 8


Let, the point be P(x, y).
Given AP = BP
⇒ AP2 = BP2
⇒ (x - 2)2 + (y - 4)2 = (x - 0)2 + (y - y)2
⇒ x2 + 4 - 4x + y2 + 16 - 8y = x2
⇒ y2 - 4x - 8y + 20 = 0

Math Olympiad Test: Coordinate Geometry- 1 - Question 9
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If the coordinates of the mid-point of the sides of a triangle are (1, 1) (2, -3), and (3, 4) what is the centroid?

Detailed Solution: Question 9



⇒ x1 + x2 = 6
y1 + y2 = 8
x2 + x3 = 2
y2 + y3 = 2
x1 + x3 = 4
y1 + y3 = -6
x1 + x2 + x3 = 12/2 = 6
x1 = 6 - 2 = 4; x2 = 2, x3 = 0
y1 + y2 + y3 = 2
y1 = 0; y2 = 8; y3 = -6
Centroid

Math Olympiad Test: Coordinate Geometry- 1 - Question 10
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What is the value of k, so that the points A(8, 1), B(3, -4), and C(2, K) are collinear?

Detailed Solution: Question 10

Given points are A(8, 1), B(3, −4) and C(2, k)
It is also said that they are collinear and hence the area enclosed by them should be 0
Area of the triangle having vertices (x1, y1), (x2, y2) and (x3, y3) 
= 1/2 |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| 
Given that area of ∆ABC = 0 
∴ 0 = 1/2 |8(-4 – k) + 3(k – 1) + 2(1 – (-4))| 
∴ 0 = 1/2 |-32 – 8k + 3k - 3 + 10| 
∴ 5k + 25 = 0 
∴ k = -5 
Hence, the value of k is -5.

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This test contains 10 MCQs on Math Olympiad Test: Coordinate Geometry- 1 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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