CUET UG 2025 — General Test Geometry

2025mcqmedium

If the points P(8,5), Q(4,8), R(0,5) and S(4,k) are the vertices of a rhombus, taken in order, then the value of k is

Official previous-year question

Held on 29 May 2025 · Verified 13 Jul 2026.

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Solution

For a rhombus, all four sides are equal in length and the diagonals bisect each other at their midpoint.

Since the vertices are given in order P→Q→R→S, the diagonals are PR and QS.

The diagonals must bisect each other, so:

Midpoint of PR = Midpoint of QS

Finding the midpoint of diagonal PR:

P = (8, 5) and R = (0, 5)

Midpoint of PR $= \left(\dfrac{8+0}{2}, \dfrac{5+5}{2}\right)$

$= (4, 5)$

Finding the midpoint of diagonal QS:

Q = (4, 8) and S = (4, k)

Midpoint of QS $= \left(\dfrac{4+4}{2}, \dfrac{8+k}{2}\right)$

$= \left(4, \dfrac{8+k}{2}\right)$

Setting the midpoints equal:

$(4, 5) = \left(4, \dfrac{8+k}{2}\right)$

The x-coordinates match. Equating the y-coordinates:

$5 = \dfrac{8+k}{2}$

$10 = 8 + k$

$k = 2$

Therefore, the value of $k = 2$ .

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Solution

For a rhombus, all four sides are equal in length and the diagonals bisect each other at their midpoint.

Since the vertices are given in order P→Q→R→S, the diagonals are PR and QS.

The diagonals must bisect each other, so:

Midpoint of PR = Midpoint of QS

Finding the midpoint of diagonal PR:

P = (8, 5) and R = (0, 5)

Midpoint of PR $= \left(\dfrac{8+0}{2}, \dfrac{5+5}{2}\right)$

$= (4, 5)$

Finding the midpoint of diagonal QS:

Q = (4, 8) and S = (4, k)

Midpoint of QS $= \left(\dfrac{4+4}{2}, \dfrac{8+k}{2}\right)$

$= \left(4, \dfrac{8+k}{2}\right)$

Setting the midpoints equal:

$(4, 5) = \left(4, \dfrac{8+k}{2}\right)$

The x-coordinates match. Equating the y-coordinates:

$5 = \dfrac{8+k}{2}$

$10 = 8 + k$

$k = 2$

Therefore, the value of $k = 2$ .

CUET UG 2025 — General Test Geometry

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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