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

Question

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

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1 year 2021-09-04T11:18:58+00:00 1 Answers 75 views 0

Answers ( )

1. 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:

$$Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$$

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

Midpoint of AC = Midpoint BD

$$\left(\dfrac{-3+6}{2},\dfrac{9+(-6)}{2}\right)=\left(\dfrac{0+a}{2},\dfrac{-3+b}{2}\right)$$

$$\left(\dfrac{3}{2},\dfrac{3}{2}\right)=\left(\dfrac{a}{2},\dfrac{-3+b}{2}\right)$$

On comparing both sides, we get

$$\dfrac{3}{2}=\dfrac{a}{2}$$

$$3=a$$

And,

$$\dfrac{3}{2}=\dfrac{-3+b}{2}$$

$$3=-3+b$$

$$3+3=b$$

$$6=b$$

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