Question

if a point A (0, 2) is equidistant from the points B ( 3, p) and C (p, 5), then find the value

Answer 1

$\sqrt{(3 - 0)^{2} + (p - 2) ^{2} } = \sqrt{(p - 0) {}^{2} + (5 - 2) {}^{2} }$
squaring both side ,
9+p^2+4-4p=p^2+9
13-4p=9
4p=4
p=1

Answer 2

AB*2=9+p*2-2×p×2+4
AC*2=p*2+9,equate both
9+p*2-4p+4=p*2+9
4p=4, p=1