Question

2. Three points of a parallelogram are (4, 3), (-4, 3), and (2, 3). Find the coordinates of the 4th point to complete the parallelogram. Please use the coordinate plane below to help find the missing point​

Answer 1

Parallelograms have equal and parallel opposite sides

The coordinates of the 4th point is (-2,3)

Let the parallelogram be ABCD, such that:

$A = (4,3)$

$B =(-4,3)$

$C = (2,3)$

A and B have the same y-coordinates, while their x-coordinates are additive inverse

This means that:

The y-coordinates of point C and point D will be the same, while their x-coordinates will be additive inverse.

For point C

We have:

$x = 2$

$y = 3$

For point D

The coordinates would be:

$x =- 2$

$y = 3$

Hence, the coordinates of D is (-2,3)

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