Question

The values of y for which the point (2, –4) is equidistant from the points (3, 8) and (–10, y), are ______.

Answer 1

The values of y for which the point (2, –4) is equidistant from the points (3, 8) and (–10, y), are –3, –5.

Explanation:

Let A(2, –4), P(3, 8), Q(–10, y). 

Equate distances AP = AQ:

(2 – 3)² + (–4 – 8)² = (2 + 10)² + (–4 – y)² 

So 1 + 144 = 144 + (y² + 8y + 16)

⇒ 145 = 160 + y² + 8y

⇒ y² + 8y + 15 = 0

⇒ (y + 5)(y + 3) = 0

Hence y = –5 or –3.