



 
Joel, Suppose you have the line segment joining A with coordinated [3, 1] and B with coordinates [5, 2], and you want to find the midpoint of this line segment. I let C be the midpoint and constructed triangles CAD and BCE using horizontal and vertical line segments. Triangles CAD and BCE are similar and BC = CA so the triangles are congruent. Thus AD = CE and hence the xcoordinate of C is midway between the xcoordinates of A and B. That is the xcoordinate of C is (5 + 3)/2 = 4. Similarly the ycoordinate of C is (2 + 1)/2 = 3/2. Now try your problem,  


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