You for your !
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 rstv and labeling the midpoints of the sides of the quadrilateral as a, b, c, and d.

To find all coordinates, we just need to observe the graph.

The coordinates of point C are (2c,d). From the graph, we notice that the x-coordinate of C is the same x-coordinate of V, because they are in the same vertical lines.

The coordinates of point D are (c,0). The problem states that D is a mid point, so basically its coordinate is half of point's V, which is c.

The slope of both AB and DC is d/c. The slope is the fraction between y-coordinate and x-coordinate. If you we calculate the slope of DC, we would have d as vertical coordinate and c as horizontal coordinate.

The slop of both AD and BC is -b/c-a. The slope between the points A(a,b) and D(c,0) is

See attached picture.

For the slope, the slope is the change in Y over the change in X.