Sum

Find the value of x, if the distance between the points (x, – 1) and (3, 2) is 5.

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#### Solution

Let P(x, – 1) and Q(3, 2) be the given points, Then,

PQ = 5 (Given)

`\Rightarrow \sqrt{(x-3)^{2}+(-1-2)^{2})=5`

`⇒ (x – 3)^2 + 9 = 5^2`

`⇒ x^2 – 6x + 18 = 25 ⇒ x^2 – 6x – 7 = 0`

⇒ (x – 7) (x + 1) = 0 ⇒ x = 7 or x = – 1

Concept: Distance Formula

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