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)

a. the residual plot for model 1 has a random pattern and is a good fit for the data.

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1