Question

A is at (2,3) and B is at (5,-2).
P is at (x,4) and PA=PB. Find the value of x.​

Answer 1

Step-by-step explanation:

Given that PA = PB

that means point P is equidistant from point A and point B

by applying the distance formula

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

$x {}^{2} + 4 - 4x + 1 = 1 + x {}^{2} - 2x + 36$

$5 - 4x = 37 - 2x$

$- 2x = 32$

$x = - 16$

Hope u understand