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Answer:
Proved
Step-by-step explanation:
Given
[tex]B =(-2,-1)[/tex]
[tex]U = (0,3)[/tex]
[tex]G = (3,2)[/tex]
[tex]S = (4,-3)[/tex]
Required
Prove BUGS is a trapezoid
Given the coordinates, to prove a trapezoid; all we need to do is to check if one pair of sides is parallel.
Taking BU and GS as a pair
First, we calculate the slope using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
For BU
[tex]B =(-2,-1)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]U = (0,3)[/tex] --- [tex](x_2,y_2)[/tex]
So, we have:
[tex]m = \frac{3 - -1}{0- -2}[/tex]
[tex]m = \frac{4}{2}[/tex]
[tex]m = 2[/tex]
For GS
[tex]G = (3,2)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]S = (4,-3)[/tex] --- [tex](x_2,y_2)[/tex]
So, we have:
[tex]m = \frac{-3-2}{4-3}[/tex]
[tex]m = \frac{-5}{1}[/tex]
[tex]m = -5[/tex]
The slope of BU and GS are not the same; hence, they are not parallel.
Taking BS and GU as a pair
Calculate the slope
For BS
[tex]B =(-2,-1)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]S = (4,-3)[/tex] --- [tex](x_2,y_2)[/tex]
So, we have:
[tex]m = \frac{-3 - -1}{4- -2}[/tex]
[tex]m = \frac{-2}{6}[/tex]
[tex]m = -\frac{1}{3}[/tex]
For GU
[tex]G = (3,2)[/tex] --- [tex](x_1,y_1)[/tex]
[tex]U = (0,3)[/tex] --- [tex](x_2,y_2)[/tex]
So, we have:
[tex]m = \frac{3-2}{0-3}[/tex]
[tex]m = \frac{1}{-3}[/tex]
[tex]m = -\frac{1}{3}[/tex]
The slope of BS and GU are the same; hence, they are parallel.
BUGS is a trapezoid because BS and GU have the same slope