CUET UG 2025 — General Test Geometry

2025mcqmedium

If the points A(3, 0), B(x, 5), C(-1, 4) and D(-2, -1) are the vertices of a rhombus, taken in order, find the value of x.

Official previous-year question

Held on 30 May 2025 · Verified 13 Jul 2026.

Options

A
-4
B
2
C
4
D
-2

Did you get this right?

Solution

The diagonals of a rhombus bisect each other at the same point.

The vertices are in order: A → B → C → D

The diagonals are:

Diagonal 1: A to C
Diagonal 2: B to D

Given: A(3, 0) and C(-1, 4)

Midpoint of AC:

$= \left(\dfrac{3 + (-1)}{2}, \dfrac{0 + 4}{2}\right)$

$= \left(\dfrac{2}{2}, \dfrac{4}{2}\right)$

$= (1, 2)$

Given: B(x, 5) and D(-2, -1)

Midpoint of BD:

$= \left(\dfrac{x + (-2)}{2}, \dfrac{5 + (-1)}{2}\right)$

$= \left(\dfrac{x - 2}{2}, \dfrac{4}{2}\right)$

$= \left(\dfrac{x - 2}{2}, 2\right)$

Since both diagonals bisect at the same point:

$(1, 2) = \left(\dfrac{x - 2}{2}, 2\right)$

The y-coordinates match.

For x-coordinates:

$1 = \dfrac{x - 2}{2}$

$2 = x - 2$

$x = 4$

Therefore, the value of $x = 4$ .

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Solution

The diagonals of a rhombus bisect each other at the same point.

The vertices are in order: A → B → C → D

The diagonals are:

Diagonal 1: A to C
Diagonal 2: B to D

Given: A(3, 0) and C(-1, 4)

Midpoint of AC:

$= \left(\dfrac{3 + (-1)}{2}, \dfrac{0 + 4}{2}\right)$

$= \left(\dfrac{2}{2}, \dfrac{4}{2}\right)$

$= (1, 2)$

Given: B(x, 5) and D(-2, -1)

Midpoint of BD:

$= \left(\dfrac{x + (-2)}{2}, \dfrac{5 + (-1)}{2}\right)$

$= \left(\dfrac{x - 2}{2}, \dfrac{4}{2}\right)$

$= \left(\dfrac{x - 2}{2}, 2\right)$

Since both diagonals bisect at the same point:

$(1, 2) = \left(\dfrac{x - 2}{2}, 2\right)$

The y-coordinates match.

For x-coordinates:

$1 = \dfrac{x - 2}{2}$

$2 = x - 2$

$x = 4$

Therefore, the value of $x = 4$ .

CUET UG 2025 — General Test Geometry

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Solution

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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