Trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph. What are the coordinates of pre-image point H?

The coordinates of pre-image point H are (3, 2).

Given that,

Trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph.

We have to determine,

What are the coordinates of pre-image point H?

According to the question,

Rotation in mathematics is a transformation that rotates a figure about a fixed point known as the center of rotation.

In rotation, there is a central point that remains fixed, and everything else rotates around that point.

The counterclockwise rotation of 180 degrees is centered at the origin. Again, as we did in the case of 90 degrees.

In the given diagram H' is located at (-3,-2).

By the rule for 180° rotation about the origin is :

(x, y) is equal to (-x, -y).

Then, the point H' located at (-3, -2) after rotation at 180 degrees the co-ordinate about the origin is,

(-3, -2) is equal to (3, 2).

Hence, the coordinates of pre-image point H are (3, 2).

For more details refer to the link given below.

link

H(3,2)

Step-by-step explanation:

The missing diagram is shown in the attachment.

The trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph.

We want to determine the coordinates of the pre-image point H.

From the diagram H' is located at (-3,-2).

We know the rule for 180° rotation about the origin is :

This means that:

Equating corresponding components, we have -x=-3.

This means that:

x=3.

Also, -y=-2, implies that y=2.

Therefore the coordinates of the pre-image point H is (3,2)