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CBSE Class 10  >  Class 10 Test  >  Olympiad Preparation  >  Math Olympiad Test: Coordinate Geometry- 4 - Class 10 MCQ

Math Olympiad Test: Coordinate Geometry- 4 - Free MCQ with solutions


MCQ Practice Test & Solutions: Math Olympiad Test: Coordinate Geometry- 4 (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- 4". 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- 4 - Question 1
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The coordinates of the third vertex of an equilateral triangle whose two vertices are at (3, 4), (–2, 3) are ________.

Detailed Solution: Question 1

Since, ΔABC is equilateral
∴ AB = AC ⇒ AB2 = AC2

⇒ (x – 3)2 + (y – 4)2
= (x + 2)2 + (y – 3)2
⇒ 5x + y – 6 = 0 ... (i)
Now, area of equilateral triangle = 
∴ Area of ΔABC = 

⇒ x – 5y = 13√3 − 17 ...(ii)
or x – 5y = −(13√3 + 17) ...(iii)
Solving (i) and (ii), we get,

Also, on solving (i) and (iii), we get

Math Olympiad Test: Coordinate Geometry- 4 - Question 2
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The vertices of a ΔABC are A(2,1), B(6, –2), C(8, 9). If AD is angle bisector, where D meets on BC, then coordinates of D are _______.

Detailed Solution: Question 2

AD is the angle bisector of ∠BAC.
So, by the angle bisector theorem in ΔABC, we have
 ...(i) 

Now, AB = 5 and AC = 10
∴ 1/2 = BD/DC [using (i)]
Thus, D divides BC in the ratio 1 : 2
∴ 

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Math Olympiad Test: Coordinate Geometry- 4 - Question 3
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Find the coordinates of the point on X-axis which are equidistant from the points (–3, 4) and (2, 5).

Detailed Solution: Question 3

Let P(x, 0) be the point on x-axis which is equidistant from points A(–3, 4) and B(2, 5)
Distance AP = Distance BP
⇒
⇒ (x + 3)2 + 16 = (x – 2)2 + 25
⇒ x2 + 9 + 6x + 16 = x2 + 4 – 4x + 25
⇒ 10x = 4 ⇒ x = 2/5
Co-ordinate of P (x, 0) is (2/5, 0).

Math Olympiad Test: Coordinate Geometry- 4 - Question 4
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In what ratio is the line segment joining the points (–3, 2) and (6, 1) is divided by Y-axis?

Detailed Solution: Question 4

We know, co-ordinates on Y-axis is (0, y). Now, let P(0, y) divides the line segment joining the points A(–3, 2) and B(6, 1) in λ : 1.

Then, 
∴ Required ratio = 1 : 2.

Math Olympiad Test: Coordinate Geometry- 4 - Question 5
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Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines)

Detailed Solution: Question 5

According to question,
Distance covered from House to Bank

Distance covered from bank to school

Distance covered from school to office

∴ Total distance covered by Ayush = 5 + 10 + 12 = 27 km
Also, Distance covered directly from House to office 
∴ Required distance = 27 – 11√5 = 2.40 km

Math Olympiad Test: Coordinate Geometry- 4 - Question 6
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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 =

Detailed Solution: Question 6

Since, centroid of triangle formed by (a, b), (b, c) and (c, a) is at the origin,
 ⇒ a + b + c = 0 ...(i)
Also, a3 + b3 + c3 – 3abc = 1/2 [a + b + c] × [(a – b)2 + (b – c)2 + (c – a)2]
⇒ a3 + b3 + c3 – 3abc = 0 (from (i))
⇒ a3 + b3 + c3 = 3abc

Math Olympiad Test: Coordinate Geometry- 4 - Question 7
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DIRECTION: Students of a school are standing in rows and columns in their playground for drill practice. A, B, C and D are the position of the four students as shown in the figure.

Q. If Mohit wants to stand in such a way that he is equidistance from each of the four students A, B, C and D then what are the coordinate of his position?

Detailed Solution: Question 7

Mohit’s position will be (7, 5).

Math Olympiad Test: Coordinate Geometry- 4 - Question 8
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DIRECTION: Students of a school are standing in rows and columns in their playground for drill practice. A, B, C and D are the position of the four students as shown in the figure.

Q. What is the difference of distance between AC and AD?

Detailed Solution: Question 8

From the given figure, Coordinates of A, B, C and D are respectively (3, 5), (7, 1), (11, 5) and (7, 9)
Distance from A to C 
Distance from A to D

∴ Required difference = 8 – 4√2 = 2.34 units

Math Olympiad Test: Coordinate Geometry- 4 - Question 9
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To raise social awareness about t he hazards of smoking, a school decided to start “No smoking campaign”. A student is asked to prepare a campaign banner in the shape of a triangle shown in the figure. If cost of 1 cm2 of banner is ₹2, find the cost of the banner.

Detailed Solution: Question 9

Area of banner
1/2= | [7(1− 1) + 1(1− 3) + 6(3 − 1)] = 5 cm2
Cost of 1 cm2 of banner = ₹2
∴ Cost of 5 cm2 of banner = 2 × 5 = ₹10

Math Olympiad Test: Coordinate Geometry- 4 - Question 10
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A well planned locality, has two straight roads perpendicular to each other. There are 5 lanes parallel to Road - I. Each lane has 8 houses as seen in figure. Chaitanya lives in the 6th house of the 5th lane and Hamida lives in the 2nd house of the 2nd lane. What will be the shortest distance between their houses?

Detailed Solution: Question 10

According to question,
Coordinates of Chaitanya’s house is (6, 5)
Coordinates of Hamida’s house is (2, 2)
∴ Shortest distance between their houses

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This test contains 10 MCQs on Math Olympiad Test: Coordinate Geometry- 4 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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