If you are given the 3 vertices of a parallelogram below, find the exact coordinates of the 4th vertex. find the coordinates for point d: a (-2, -1) b (2, 1) c (0, -3)d (x, y) explain all the steps and show all work!

  (-4,-5)                        

Step-by-step explanation:

Here ABCD is a parallelogram,

Where A≡(-2,-1), B≡(2,1), C≡(0,-3) and D≡(x,y)

By the property of parallelogram,

AB║CD, AD║BC, AB = CD and AD=BC

If AB ║ CD

⇒ Slope of AB = Slope of CD

⇒

⇒

⇒

⇒ ------ (1)

Now, AB = CD

From equation (1)

⇒ y = -1 or -5

Again by equation (1)

for y = -1, x = 4

For y = -5, x = -4

Thus the coordinate of D are (4,-1) or ( -4,-5)

But for D≡(4,-1), AD∦BC

While For D≡(-4,-5) AD ║ BC

Thus the coordinates of D are ( -4,-5)