Question

If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is ______.

Options

• -7 or -1

• -7 or 1

• 7 or 1

• 7 or -1

Answer 1

If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is 7 or -1.

Explanation:

We have `sqrt((x - 3)^2 + (- 1 - 2)^2)` = 5

⇒ (x – 3)² + 9 = 25

⇒ x² – 6x + 9 + 9 = 25

⇒ x² -6x – 7 = 0

⇒ (x – 7)(x + 1) = 0

⇒ x = 7 or x = -1