Question

Which points are on the perpendicular bisector of the given segment? Check all that apply.

(−8, 19)
(1, −8)
(0, 19)
(−5, 10)
(2, −7)

Answer 1

I don't see the endpoints of the segment in your question — could you provide the coordinates of the segment's two endpoints?

How to check once you have them:
- A point P = (x,y) lies on the perpendicular bisector of segment AB (A=(x1,y1), B=(x2,y2)) iff P is equidistant from A and B:
(x−x1)^2 + (y−y1)^2 = (x−x2)^2 + (y−y2)^2.
- Equivalently, compute the midpoint M = ((x1+x2)/2, (y1+y2)/2) and the slope m of AB = (y2−y1)/(x2−x1). The perpendicular bisector is the line through M with slope −1/m (or vertical if m=0, or horizontal if m is infinite). Check which given points lie on that line.

Send the endpoints and I will test the five given points.