A telecommunication company wants to build a relay tower that is equidistant from two towns. On a map, Town A is located at (2, 6) and Town B is located at (10,0).

Question

Use an equation to represent the possible locations of the tower.

Answer 1

midpoint of (2,6) and (10,0) is (6,3)

a line through the two points has slope =(6-0)/(2-10) = -6/8=-3/4

slope of the perpendicular line has the negative inverse, 4/3

y-3 =(4/3)(x-6) = (4/3)x -8

y = (4/3)x -5 is the equation of the line which includes all points equidistant from (2,6) and (10,0)