Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex.
(-3,9)
(0,-3) (6,-6)

Given:

The three vertices of the parallelogram are (-3,9), (0,-3), (6,-6).

To find:

The fourth vertex of the parallelogram.

Solution:

Consider the three vertices of the parallelogram are A(-3,9), B(0,-3), C(6,-6).

Let D(a,b) be the fourth vertex.

Midpoint formula:

We know that the diagonals of a parallelogram bisect each other. So, the midpoints of both diagonals are same.

Midpoint of AC = Midpoint BD

On comparing both sides, we get

And,

Therefore, the fourth vertex of the parallelogram is (3,6).

answer:     true

step-by-step explanation: