if lm =mp then m must be the mid point of lp

Answer 1

Midpoint of a line segment =

Definition: A point on a line segment that divides it into two equal parts

The halfway point of a line segment

Since the "midpoint" is halfway between two points, it mentions the line segment between those two points.

In this case, lp is a line segment with the point m on the line between them -- at the halfway point.

Note: It may be that lm = mp and m is NOT on the line segment lp.