# On a coordinate plane, a trapezoid has points H prime (negative 3, negative 2), J prime (negative 2, negative 3), K prime (negative

On a coordinate plane, a trapezoid has points H prime (negative 3, negative 2), J prime (negative 2, negative 3), K prime (negative 3, negative 4), G prime (negative 5, negative 2). 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? (2, 3) (–2, 3) (3, 2) (3, –2)

## This Post Has 5 Comments

1. skylex says:

when a point M (h, k) is rotated about the origin O through 180° in anticlockwise or clockwise direction, it takes the new position M' (-h, -k). The signs of the coordinates change .

In the given graph point H' is (-3,-2) .The pre image of this point will be point H .Point H will have coordinates which will have signs of both coordinates opposite to that  of point H'.

Coordinates of point H will be (3,2)

Step-by-step explanation:

2. harringtonrob16 says:

(3,2)

Hope this helps

3. srtero says:

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 :

$(x,y)\to (-x,-y)$

This means that:

$( - 3, - 2) = (-x,-y)$

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)

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

4. destinybonmer says:

when a point M (h, k) is rotated about the origin O through 180° in anticlockwise or clockwise direction, it takes the new position M' (-h, -k). The signs of the coordinates change .

In the given graph point H' is (-3,-2) .The pre image of this point will be point H .Point H will have coordinates which will have signs of both coordinates opposite to that  of point H'.

Coordinates of point H will be (3,2)

5. jeff6284 says:

(2,3)

Step-by-step explanation: