Quadrilateral abcd has coordinates a(-5,4),b(0,6),c(3,-1), and d(-2,-3). use the midpoint formula to determine if the figure is a parallelogram and why.

To solve this problem you must apply the proccedure shown below:

 1. You have that the 1uadrilateral abcd has coordinates A(-5,4),B(0,6),C(3,-1), and D(-2,-3).

 2. Now, you must apply the formula for calculate the midpoint, which is:

 M=(x2+x1/2, y2+y1/2)

 3. Therefore, you have:

 M1=(3+(-5)/2, -1+4/2)
 M1=(-2/2, 3/2)
 M1=(-1,3/2)

 M2=(-2+0/2, -3+6/2)
 M2=(-1, 3/2)

 M1=M2

 4. Then the answer is:

 The figure is a parallelogram, because its diagonals bisect each other.