Question

find the relation between x and y such that the point (x,y) is equidistant from points (-1,8) and(3,4).
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Answer 1

Step-by-step explanation:

Let P(x,y) be equidistant from the point Q(-1,8) and R(3,4) .

Given : P is equidistant from Q and R i.e.. PR = PQ

Now, PR = PQ

Square both the side (here we do square to avid under root and make the equation simple)

(PR)² = (PQ)²

[x - (-1)]² + [ y-8]² = [x - 3]² + [y - 4]²

(x + 1)² + (y - 8)² = (x - 3)² + ( y- 4)²

By solving this eq we get,

8x - 8y = -40

8(x - y ) = -40

x - y = -5