Question

Remy rotates figure EFGH 180 degrees counterclockwise around the origin to form figure E'F'G'H and then translates the image 6 units down to form figure E'' F'' G'' H''. what are the coordinates of vertex F''?

Answer 1

To find the coordinates of vertex F'', we can follow these steps: apply the rotation to the original coordinates of F and then apply the translation to the rotated coordinates.

Step-by-step explanation:

To find the coordinates of vertex F'', we need to understand the transformations applied to the original figure.

First, a 180-degree counterclockwise rotation around the origin is applied to form figure E'F'G'H'. This means that each point's coordinates (x, y) are transformed to (-x, -y).

Next, the figure is translated 6 units down to form figure E''F''G''H''.

This means that each point's coordinates (x, y) are transformed to (x, y-6).

To find the coordinates of vertex F'', we can follow these steps:

1. Apply the rotation to the original coordinates of F: (-2, 0)
2. Apply the translation to the rotated coordinates: (-2, 0) -> (-2, -6)

Therefore, the coordinates of vertex F'' are (-2, -6).