1)Take for example (0,1) and (1,0) to illustrate.
2)Plot these point
3)Draw a line segment from (0,1) down and draw a line segment from (1,0) left.
4)Those intersect as (0,0)
5)By similar triangles if (x,y) is midpoint then x is midpoint of vertical line segment and y is midpoint of horizontal line segment.