Answer:
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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 = [tex]\frac{x1 + x2}{2}[/tex]
Ym = [tex]\frac{y1 + y2}{2}[/tex]
Coordinates of point A
Xm = [tex]\frac{0 + 2a}{2} = \frac{2a}{2} = a[/tex]
Ym = [tex]\frac{0 + 2b}{2} = \frac{2b}{2} = b[/tex]
A ( a, b)
Coordinates of point B
Xm = [tex]\frac{2a + 2c}{2} = \frac{2(a + c)}{2} = a + c[/tex]
Ym = [tex]\frac{2b + 2d}{2} = \frac{2(b + d)}{2} = b + d[/tex]
B ( a + c , b + d)
Coordinates of point C
Xm = [tex]\frac{2c + 2c}{2} = \frac{2(c + c)}{2} = 2c[/tex]
Ym = [tex]\frac{2d + 0}{2} = \frac{2d}{2} = d[/tex]
C (2c , d)
Coordinates of point D
Xm = [tex]\frac{2c + 0}{2} = \frac{2c}{2} = c[/tex]
Ym = [tex]\frac{0 + 0}{2} = \frac{0}{2} = 0[/tex]
D (c, 0)
Slope of AB and DC is
Formula
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
Substitution
Slope AB = [tex]\frac{b + d - b}{a + c - a} = \frac{d}{c}[/tex]
Slope CD = [tex]\frac{0 - d}{c - 2c} = \frac{-d}{-c} = \frac{d}{c}[/tex]
Slope AB = slope CD = d/c
