Question

The distance between the points (3, 1) and (0, x) is 5. Find x.

Answer 1

It is given that the distance between the points A (3, 1) and B (0, x) is 5.
∴ AB = 5
AB² = 25
(0 - 3)² + (x - 1)² = 25
9 + x² + 1 - 2x = 25
x² - 2x - 15 = 0
x² - 5x + 3x - 15 = 0
x(x - 5) + 3(x - 5)  = 0
(x - 5)(x + 3) = 0
x = 5, -3