



 
Hi Jane, This is an exercise with similar triangles. Suppose A and B are points in the plane and you wish to determine the coordinates of M the midpoint of the line segment AB. In the diagram below the line segment AC is parallel to the xaxis and the line segments CB and PM are parallel to the yaxis. Triangles BAC and MAP are similar so
But BA = 2MA so
or
Thus P is the midpoint of AC and hence the xcoordinate of P, which is also the xcoordinate of M, is the average of the xcoordinates of A and B. A similar argument shows that the ycoordinate of M is the average of the ycoordinates of A and B. For an example suppose A has coordinates (2, 3) and B has coordinates (4, 5). The midpoint of the line segment AB then has xcoordinate (2 + 4)/2 = 1 and ycoordinate (3 + 5)/2 = 4. I hope this helps,  


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