Question

MATH HELP PLEASE

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

Answer 1

calculate the slopes of the lines using the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

(x₁, y₁ ) = A(- 4, - 1) and (x₂, y₂ ) = B(-1, 2 )

`m_(AB)` =
`(2+1)/(-1+4)` =
`(3)/(3)` = 1

(x₁, y₁ ) = B(-1, 2) and (x₂, y₂ ) = (5, 1)

`m_(BC)` =
`(x1-2)/(5+1)` = -
`(1)/(6)`

(x₁, y₁) = C(5, 1 ) and (x₂, y₂ ) = D(1, - 3)

`m_(CD)` =
`(-3-1)/(1-5)` =
`(-4)/(-4)` = 1

(x₁, y₁) = A(- 4, - 1) and (x₂, y₂) = D(1, - 3 )

`m_(AD)` =
`(-3+1)/(1+4)` = -
`(2)/(5)`

Quadrilateral ABCD is not a parallelogram since only one pair of opposite sides is parallel , that is AB and CD