WILL GIVE BRAINLIEST! Prove that a quadrilateral ABCD with vertices A(–1, –2), B( 2, –5), C(1, –2), and D( –2, 1) is a parallelogram. Find the point of intersection of the diagonals of parallelogram ABCD. Provide your complete solutions and proofs in your paper homework and enter the numeric answers online.

Step-by-step explanation:

To prove a quadrilateral a parallelogram we prove,

1). Length of opposite sides are equal.

2). Slopes of the opposite sides are same.

Length of AB =

                      =

                      =

Length of BC =

                      =

Length of CD =

                      =

Length of AD =

                      =

Therefore, AB = CD and BC = AD (Opposite sides are equal in length)

Slope of AB =

                    =

                    = -1

Slope of BC =

                    = -3

Slope of CD =

                    = -1

Slope of AD =

                    = -3

Slope of AB = slope of CD and slope of BC = slope AD

Therefore, AB║CD and BC║AD

Hence ABCD is a parallelogram

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!