Question

Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex.

Answer 1

Answer:

(1,-8)

Step-by-step explanation:

We were given three vertices of a parallelogram to be:

(3,-2), (-1,-4), (5,-6).

After plotting the points as shown in the attachment, we realize (3,-2) and (-1,-4) form a diagonal.

The midpoint of this diagonal using the midpoint formula is  

is  

Recall that, the midpoint of both diagonals are the same.

Let the fourth point have coordinates (x,y).

Then using the midpoint formula again with (3,-2), we have:

This implies that:

and  

and  

x=1 and y=-8

The coordinates of the fourth point are:

(1,-8)