Question

Give one pair of values of x and y such that (x,y) is equidistant from the points (-1,8) and (3,4). Justify your steps.

Answer 1

The value of x is 1 and y is 6 such that (1,6) equidistance from the points (-1,8) and (3,4)

Step-by-step explanation:

Let the point P(x,y) equi-distance from A(-1,8) and B(3,4)

So, PA=PB

$\sqrt{(x+1)^2+(y-8)^2}=\sqrt{(x-3)^2+(y-4)^2}$

Square both sides to cancel square root

$x^2+1+2x+y^2+64-16y=x^2+9-6x+y^2+16-8y$

$2x-16y+65=-6x-8y+25$

$8x-8y=-40$

$x-y=-5$

All the points lie on line will equ-distance from (-1,8) and (3,4)

Take y = 6

x = 1

Point (1,6)

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