Question

A triangle, △ABC, is rotated 90° counterclockwise, reflected across the x−axis, and then reflected across the y−axis. Select True or False for each statement.

1. Rotating △ABC 180° clockwise is an equivalent transformation. True or False?
2. Rotating △ABC 270° clockwise is an equivalent transformation. True or False?
3. Reflecting △ABC across the y-axis is an equivalent transformation. True or False?
Please help!!

Answer 1

Rotating 180° and 270° clockwise are not equivalent transformations to the original sequence, but reflecting △ABC across the y-axis is an equivalent transformation.

Step-by-step explanation:

1. Rotating △ABC 180° clockwise is false because when a figure is rotated 180° clockwise, the vertices will end up in different positions than when it is rotated 90° counterclockwise, reflected across the x-axis, and then reflected across the y-axis.

2. Rotating △ABC 270° clockwise is false because when a figure is rotated 270° clockwise, the vertices will end up in different positions than when it is rotated 90° counterclockwise, reflected across the x-axis, and then reflected across the y-axis.

3. Reflecting △ABC across the y-axis is true because reflecting a figure across the y-axis is the same as reflecting it across the x-axis and then rotating it 180° counterclockwise.