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# Kim-Ly is writing a coordinate proof to show that the midpoints of a quadrilateral are the vertices of a parallelogram.

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Kim-Ly is writing a coordinate proof to show that the midpoints of a quadrilateral are the vertices of a parallelogram. She starts by assigning coordinates to the vertices of quadrilateral RSTVquadrilateral RSTV and labeling the midpoints of the sides of the quadrilateral as A, B, C, and D.

Enter the answers, in simplified form, in the boxes to complete the proof.

The coordinates of point A are (a, b) .

The coordinates of point B are (a + c, b + d).

The coordinates of point C are (    , d). <-- answer

The coordinates of point D are (    ,   ).  <--- answer

The slope of both AB¯¯¯¯¯and DC¯¯¯¯¯ is (________) .  <-- answer

Because both pairs of opposite sides are parallel, quadrilateral ABCD is a parallelogram.

Nov 14, 2017

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The coordinates of C are  (2c, d)

The coordinates of D are  ( c, 0 )

The slope of AB and DC =

[ (b + d) - b] / [ (a + c) - a ]  =  [ (d - 0)] / [ 2c - c]  =   [ d / c ]

The slope of  AD and BC =

[ ( b - 0)] /  [(a - c} =  [ (b + d) - d ] / [  (a + c) - 2c]  =  [ b / (a - c) ]

Nov 14, 2017