CUET UG 2025 — General Test Geometry

2025mcqmedium

If the two vertices of a triangle are (5,4), and (-2,4) and the centroid is (5,6), then the third vertex is:

Official previous-year question

Held on 15 May 2025 · Verified 13 Jul 2026.

Options

A
(10, 12)
B
(-10, 12)
C
(12, -10)
D
(12, 10)

Did you get this right?

Solution

The centroid of a triangle with vertices $(x_1, y_1)$ , $(x_2, y_2)$ , and $(x_3, y_3)$ is given by:

Centroid $= \left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right)$

Given vertices: $(5, 4)$ , $(-2, 4)$ , and $(x, y)$

Given centroid: $(5, 6)$

For the $x$ -coordinate of the centroid:

$5 = \frac{5 + (-2) + x}{3}$

$5 = \frac{3 + x}{3}$

$15 = 3 + x$

$x = 12$

For the $y$ -coordinate of the centroid:

$6 = \frac{4 + 4 + y}{3}$

$6 = \frac{8 + y}{3}$

$18 = 8 + y$

$y = 10$

Therefore, the third vertex is $(12, 10)$ .

Your note

CUET UG Geometry in other years

Geometry 2024 Geometry 2023 Geometry 2022

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CUET UG 2025 — General Test Geometry

2025mcqmedium

If the two vertices of a triangle are (5,4), and (-2,4) and the centroid is (5,6), then the third vertex is:

Official previous-year question

Held on 15 May 2025 · Verified 13 Jul 2026.

Options

A
(10, 12)
B
(-10, 12)
C
(12, -10)
D
(12, 10)

Did you get this right?

Solution

The centroid of a triangle with vertices $(x_1, y_1)$ , $(x_2, y_2)$ , and $(x_3, y_3)$ is given by:

Centroid $= \left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right)$

Given vertices: $(5, 4)$ , $(-2, 4)$ , and $(x, y)$

Given centroid: $(5, 6)$

For the $x$ -coordinate of the centroid:

$5 = \frac{5 + (-2) + x}{3}$

$5 = \frac{3 + x}{3}$

$15 = 3 + x$

$x = 12$

For the $y$ -coordinate of the centroid:

$6 = \frac{4 + 4 + y}{3}$

$6 = \frac{8 + y}{3}$

$18 = 8 + y$

$y = 10$

Therefore, the third vertex is $(12, 10)$ .

Your note

CUET UG Geometry in other years

Geometry 2024 Geometry 2023 Geometry 2022

Keep practicing Geometry

Work through every CUET UG Geometry PYQ, year by year.

Browse all General Test topics

CUET UG 2025 — General Test Geometry

Options

Did you get this right?

Solution

Your note

CUET UG Geometry in other years

More CUET UG Geometry questions

Other General Test topics for CUET UG

General Knowledge

Logical Reasoning

Arithmetic

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CUET UG 2025 — General Test Geometry

Options

Did you get this right?

Solution

Your note

CUET UG Geometry in other years

More CUET UG Geometry questions

Other General Test topics for CUET UG

General Knowledge

Logical Reasoning

Arithmetic

Quantitative Reasoning

Current Affairs

Keep practicing Geometry