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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.

The answer to your question is below

Step-by-step explanation:

Data

Vertices of a quadrilateral

R (0,0)

S (2a, 2b)

T (2c, 2d)

V (2c, 0)

Process

1.- Find the coordinates of the parallelogram using the next formulas

Xm =

Ym =

Coordinates of point A

Xm =

Ym =

A ( a, b)

Coordinates of point B

Xm =

Ym =

B ( a + c , b + d)

Coordinates of point C

Xm =

Ym =

C (2c , d)

Coordinates of point D

Xm =

Ym =

D (c, 0)

Slope of AB and DC is

Formula

Substitution

Slope AB =

Slope CD =

Slope AB = slope CD = d/c