Hugo is writing a coordinate proof to show that the midpoints of a quadrilateral are the vertices of a parallelogram. He starts
by assigning coordinates to the vertices of quadrilateral RSTV and labeling the midpoints of the sides of the quadrilateral as A, B, C, and D. Quadrilateral R S T V in a coordinate plane with vertex R at 0 comma 0, vertex S in the first quadrant at 2 a comma 2b, vertex T also in the first quadrant at 2 c comma 2 d, and vertex V on the positive side of the x-axis at 2 c comma 0. Point A is between points R and S, point B is between points S and T, point C is between points T and V, and point D is between points R and V. Enter the answers, in simplified form, in the boxes to complete the proof. The coordinates of point A are ( , ). The coordinates of point B are ( , ). The coordinates of point C are (2c, d) . The coordinates of point D are (c, 0) . The slope of both AB¯¯¯¯¯ and DC¯¯¯¯¯ is . The slope of both AD¯¯¯¯¯ and BC¯¯¯¯¯ is −bc−a . Because both pairs of opposite sides are parallel, quadrilateral ABCD is a parallelogram.
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