Question

The coordinates of the vertices of quadrilateral ABCD are A(0, −4) , B(−4, 3) , C(3, 4) , and D(6, −1) . Drag and drop the choices into each box to correctly complete the sentences. The slope of AB¯¯¯¯¯ is , the slope of BC¯¯¯¯¯ is , the slope of CD¯¯¯¯¯ is , and the slope of AD¯¯¯¯¯ is . Quadrilateral ABCD is because .

Answer 1

AB -7/4, BC 1/7, CD -5/3, and AD 1/2

neither a parallelogram nor a trapezoid because

neither pair of opposite sides are parallel

Explanation:

Answer 2

The slope of AB is -7/4, the slope of BC is 1/7 , the slope of CD is 5/3, and the slope of AD is 2. So, Quadrilateral ABCD is neither a parallelogram nor a trapezoid because neither pair of opposite sides are parallel.

Explanation:

Since, a quadrilateral having,

One pair of parallel opposite sides is Trapezoid,

While, having two pair of parallel opposite sides is parallelogram.

Since, the slope of a line segment having the end points
`(x_1, y_1)` and
`(x_2, y_2)` is,

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

Here, the vertices of the quadrilateral ABCD are A(0, −4) , B(−4, 3) , C(3, 4) , and D(6, −1),

Slope of AB =
`(3+4)/(-4-0)=-(7)/(4)`

Slope of BC =
`(4-3)/(3+4)=(1)/(7)`

Slope of CD =
`(-1-4)/(6-3)=-(5)/(3)`

Slope of AD =
`(-1+4)/(6-0)=(3)/(6)=2`

Hence, Quadrilateral ABCD is neither a parallelogram nor a trapezoid because neither pair of opposite sides are parallel.