Can you find the equidistant from three points?

Question

Can you find the equidistant from the three points (0,3), (-8,3), and (-8,-5)?

Answer 1

We need to find the perpendicular bisectors of any two of the three line segments with the endpoints given. Then we can find the pt of intersection of those two perpendicular bisectors (recall that all points on the perpendicular bisector of a segment are equidistant from its endpts).

Given these pts, that is pretty easy: (0,3) and (-8,3) have the same y-coordinate so that segment is horizontal and the perp bisector is the vertical line thru the avg of the x-coords, namely x = -4.

Similarly, (-8,3) and (-8,-5) are the endpts of a horizontal line segment whose perp bisector is y = -1.

(-4,-1) is equidistant from all three given pts.