Question

Prove

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

Answer 1

Proved

Explanation:

Given

`B =(-2,-1)`

`U = (0,3)`

`G = (3,2)`

`S = (4,-3)`

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:

`m = (y_2 - y_1)/(x_2 - x_1)`

For BU

`B =(-2,-1)` ---
`(x_1,y_1)`

`U = (0,3)` ---
`(x_2,y_2)`

So, we have:

`m = (3 - -1)/(0- -2)`

`m = (4)/(2)`

`m = 2`

For GS

`G = (3,2)` ---
`(x_1,y_1)`

`S = (4,-3)` ---
`(x_2,y_2)`

So, we have:

`m = (-3-2)/(4-3)`

`m = (-5)/(1)`

`m = -5`

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

`B =(-2,-1)` ---
`(x_1,y_1)`

`S = (4,-3)` ---
`(x_2,y_2)`

So, we have:

`m = (-3 - -1)/(4- -2)`

`m = (-2)/(6)`

`m = -(1)/(3)`

For GU

`G = (3,2)` ---
`(x_1,y_1)`

`U = (0,3)` ---
`(x_2,y_2)`

So, we have:

`m = (3-2)/(0-3)`

`m = (1)/(-3)`

`m = -(1)/(3)`

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