Question

The coordinates of the vertices of quadrilateral ABCD are A(-1, -1), B(-3, 3), C(1, 5), and D(5, 2).

Answer blank #1: The slope of AB is ______

Answer blank #2: The slope of BC is ______

Answer blank #3: The slope of CD is ______

Answer blank #4: The slope of AD is ______

Answer blank #5: Quadrilateral ABCD is a _________ (choose: trapezoid or parallelogram)

For answer blank #5 make sure you spell your answer correctly!

Answer 1

Explanation:

Given that coordinates of the vertices of quadrilateral ABCD are A(-1, -1), B(-3, 3), C(1, 5), and D(5, 2).

Slope of line is given as

`slope = ( Yj - Yi )/( Xj - Xi )`

Using above formula,

The slope of AB is
`S1 =( Yj - Yi )/( Xj - Xi )`

`S1 = (3-(-1))/((-3)-(-1))`

`S1 = (4)/(-2) = -2`

The slope of BC is
`S2 = ( Yj - Yi )/( Xj - Xi )`

`S2 = (5-3)/(1-(-3))`

`S2 = (2)/(4) = (1)/(2)`

The slope of CD is
`S3 = ( Yj - Yi )/( Xj - Xi )`

`S3 = (2-5)/(5-1)`

`S3 = (-3)/(4)`

The slope of AD is
`S4 = ( Yj - Yi )/( Xj - Xi )`

`S3 = ((-1) - 2)/((-1) - 5)`

`S3 = (-3)/(-6) = (1)/(2)`

You can see that Only Line BC and Line AD are parallel.

Therefore, Quadrilateral ABCD is a Trapezoid.