CUET UG 2025 — General Test Geometry

2025mcqmedium

If the distance between the points (2, -2) and (5, k) is 5 units, then one of the possible values of k shall be which of the following?

Official previous-year question

Held on 2 Jun 2025 · Verified 13 Jul 2026.

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Solution

The distance between points (2, -2) and (5, k) is 5 units.

Using the distance formula:

$\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$5 = \sqrt{(5 - 2)^2 + (k - (-2))^2}$

$5 = \sqrt{(3)^2 + (k + 2)^2}$

$5 = \sqrt{9 + (k + 2)^2}$

Squaring both sides:

$25 = 9 + (k + 2)^2$

$(k + 2)^2 = 16$

Taking the square root of both sides:

$k + 2 = \pm 4$

This gives two possible values:

$k + 2 = 4$

$k = 2$

$k + 2 = -4$

$k = -6$

The possible values of k are 2 and -6.

Therefore, one of the possible values of k is 2.

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CUET UG 2025 — General Test Geometry

2025mcqmedium

If the distance between the points (2, -2) and (5, k) is 5 units, then one of the possible values of k shall be which of the following?

Official previous-year question

Held on 2 Jun 2025 · Verified 13 Jul 2026.

Options

Did you get this right?

Solution

The distance between points (2, -2) and (5, k) is 5 units.

Using the distance formula:

$\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$5 = \sqrt{(5 - 2)^2 + (k - (-2))^2}$

$5 = \sqrt{(3)^2 + (k + 2)^2}$

$5 = \sqrt{9 + (k + 2)^2}$

Squaring both sides:

$25 = 9 + (k + 2)^2$

$(k + 2)^2 = 16$

Taking the square root of both sides:

$k + 2 = \pm 4$

This gives two possible values:

$k + 2 = 4$

$k = 2$

$k + 2 = -4$

$k = -6$

The possible values of k are 2 and -6.

Therefore, one of the possible values of k is 2.

Your note

CUET UG Geometry in other years

Geometry 2024 Geometry 2023 Geometry 2022

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

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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