Answered

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Prove

that BUGS is a trapezoid with coordinates B(-2,-1), U(0,3), G(3,2) and S(4,-3).

Sagot :

MrRoyal

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

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