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# Trapezoid ABCD has vertices

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Trapezoid ABCD has vertices A(-1,0), B(0,2), C(m,4)  and D(k,0), with m > 0  and k > 0 . The line y = -x + 4 is perpendicular to the line containing side CD , and the area of trapezoid ABCD is 36 square units. What is the value of k?

Nov 13, 2020

#1
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Trapezoid ABCD has vertices A(-1,0), B(0,2), C(m,4)  and D(k,0), with m > 0  and k > 0 . The line y = -x + 4 is perpendicular to the line containing side CD , and the area of trapezoid ABCD is 36 square units. What is the value of k?

Hello Guest!

$$m_{ab}=\frac{2-0}{0-(-1)}$$

$$m_{ab}=2$$

$$y_{dc}=2(x-k)+0\\ y_{dc}=2(x-m)+4\\ 2x-2k=2x-2m+4\\2k=2m-4\\ k=m-2$$

to be continued

!

Nov 14, 2020
edited by asinus  Nov 15, 2020