Question

If Q (0, 1) is equidistant from P (5, –3) and R (x, 6), the positive value of x is

(a) 5

(b) 4

(c) 2

(d) 8

Answer 1

Correct option is (b) 4

As given Q(0, 1) is equidistant from P(5, −3) and R(x, 6)

⇒ PQ = QR

⇒ \(\sqrt{(0-5)^2 + (1 - (-3))^2} = \sqrt{(x - 0)^2 + (1 - 6)^2}\)

[By using distance formula = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)]

⇒ 25 + 16 = x² + 25

⇒ 41 = x² + 25

⇒ x² = 16

⇒ x = 4