Please can u show me step by step how to solve this

Question

Determine whether the point T(2,-1) lies on the right bisector of the line segment with endpoints U(3,5) and V(-3,-1).

Answer 1

If "right bisector" means perpendicular bisector, then T lies on the perpendicular bisector of UV if and only if T is equidistant from U and V.

 

Distance from T to U:  √[(2-3)² + (-1-5)²] = √37

 

Distance from T to V:  √[(2-(-3))² + (-1-(-1))²] = 5

 

So, T is NOT on the perpendicular bisector of UV.