Question

Find the linear relation between xand y such that P(x, y) is equidistant from the points A(1, 4) and B(–1, 2).

Answer 1

The answer might be C(0,3)

Answer 2

Answer: x+y=3

Step-by-step explanation:

Given: P(x,y) equidistant from A(1,4) and B(-1,2)

therefore,

AP=PB

using the distance formula on both LHS and RHS and squaring it,

(x-1)^2 +(y-4)^2 = (x+1)^2 +(y-2)^2

x^2-2x+1+y^2-8y+16 = x^2+2x+1+y^2-4y+4

cancelling and simplifying we get,

4x+4y= 17-5

4(x+y)=12

x+y=12/4

x+y=3

so the answer is x+y=3