The point (4, y) is equidistant from (2, 6) and (9, -1). Find y.

Answer 1

A nice way to answer is to find midpoint of line segment (2,6) and (9,-1) aka (11/2,5/2)

know slope of perpendicular line to segment is reciprocal if line segment slope

perpendicular slope is 1 since line slope is -1.

the perpendicular line trough the midpoint will always have only points equal from end points

perpendicular line through midpoint equation is ,,,,,,,1=(y-5/2)/(x-11/2)

or y=x-3.

when x=4, y=1

check does (4-2)²+(1-6)²=(9-4)²+(-1-1)²,,,,,yes

so (4,1) is equal length from (2,6) and (9,-1)

Answer 2

(2 - 4)² + (6 - y)² = (9 - 2)² + (-1 -6)²