You cannot. A ray is infinite in one direction and so the midpoint would be infinitely far in that direction.
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It is called a bisector.
Theorem: The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side. Proof: Consider the triangle ABC with the midpoint of AB labelled M. Now construct a line through M parallel to BC.
With a straight-edge and a compass:Swing arcs from each end of the segment with the compass (without changing the settings)Connect the intersections of these arcs.The resultant is a perpendicular bisector of the segment.
it gives you the midpoint of the line segment you use the formula for
A midpoint of anything is the point exactly halfway between the beginning point and the end point. So logically, it is the "midpoint".