Question

The coordinates of the vertices of​ quadrilateral ABCD ​ are A(−4, −1) , B(−1, 2) , C(5, 1) , and D(1, −3) . 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 a parallelogram because .

Answer 1

Part 1)
`m_A_B=1`

Part 2)
`m_B_C=-(1)/(6)`

Part 3)
`m_C_D=1`

Part 4)
`m_A_D=-(2)/(5)`

Explanation:

we know that

In a parallelogram opposite sides are parallel and congruent

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

we have

A(−4, −1) , B(−1, 2) , C(5, 1) , and D(1, −3)

step 1

Find the slope AB

substitute in the formula

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

`m=(3)/(3)`

`m_A_B=1`

step 2

Find the slope BC

substitute in the formula

`m=(1-2)/(5+1)`

`m=(-1)/(6)`

`m_B_C=-(1)/(6)`

step 3

Find the slope CD

substitute in the formula

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

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

`m_C_D=1`

step 4

Find the slope AD

substitute in the formula

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

`m=(-2)/(5)`

`m_A_D=-(2)/(5)`

step 5

Compare the slopes

Remember that

If two lines are parallel, then their slopes are the same

so

AB is parallel to CD

BC is not parallel to AD

therefore

Quadrilateral ABCD is not a parallelogram because the opposite sides are not parallel