Question

Please answer one question asap A(-4,3) B(2,-1) D(-4,-1) C(2,-5)

Answer 1

Answer:

Step-by-step explanation:

Vertices of the given quadrilateral are A(-4, 3), B(2, -1), C(2, -5) and D(-4, -1)

Since, slope of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

Slope = $\frac{y_2-y_1}{x_2-x_1}$

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

                    = $-\frac{2}{3}$

Slope of AD = $\frac{3+1}{-4+4}$

                    = Not defined (Parallel to y-axis)

Slope of DC = $\frac{-5+1}{2+4}$

                     = $-\frac{2}{3}$

Slope of BC = $\frac{-1+5}{2-2}$

                   = Not defined (Parallel to y-axis)

Slope of AB = slope of DC = $-\frac{2}{3}$

Slope of BC = slope of AD = Not defined (parallel to y-axis)

As per property of a parallelogram,

"Opposite sides of a parallelogram are parallel and equal in measure"                  

Therefore, ABCD is a parallelogram.