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 )

$m_{AB}$ = $\frac{2+1}{-1+4}$ = $\frac{3}{3}$ = 1

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

$m_{BC}$ = $\frac{x1-2}{5+1}$ = - $\frac{1}{6}$

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

$m_{CD}$ = $\frac{-3-1}{1-5}$ = $\frac{-4}{-4}$ = 1

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

$m_{AD}$ = $\frac{-3+1}{1+4}$ = - $\frac{2}{5}$

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