The distance between two points (-6, y) and (18, 6) is 26 units. Find the value of y.

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SSC CGL Memory Based Test (7th Dec 2022 Shift 1)

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Answer 1

Given:

The distance between two points (-6, y) and (18, 6) is 26 units.

Formula used:

D = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Where,

The distance between two points (x₁, y₁) and (x₂, y₂) is D units.

Calculation:

The distance between two point = 26 units

The value of the first co-ordinate = (x₁, y₁) = (-6, y)

The value of the second co-ordinate = (x2, y2) = (18, 6)

According to the question,

⇒ D = \(\sqrt{(18-(-6))^2 + (6-y)^2} \)

⇒ 26 = \(\sqrt{(24)^2 + (6-y)^2} \)

Squaring on both sides of the equation.

⇒ 676 = 24² + (6 - y)²

⇒ 676 = 576 + (6 - y)2

⇒ 100 = (6 - y)2

⇒ 10² = (6 - y)2

Taking square root on both sides of the equation.

⇒ 10 = 6 - y

⇒ y = -4

∴ The required answer is -4.

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