Question

4 figure ( r cong r ). describe a sequence of three transformations that can be performed on figure ( r ) to show this. show your work.

Explanation:

Step1: Rotate 90° counterclockwise

Rotate figure \( R \) 90° counterclockwise about the origin. This changes the orientation of the figure to align with the general direction of \( R''' \).

Step2: Translate vertically

Translate the rotated figure up by 6 units (to move it from the lower y - range to the upper y - range near \( R''' \)). The vertical distance between the original \( R \) (around \( y=-5 \)) and \( R''' \) (around \( y = 1 \)) is \(1-(-5)=6\).

Step3: Translate horizontally

Translate the vertically translated figure to the right by 9 units. The horizontal distance between the rotated and vertically translated figure (starting from around \( x=-6 \)) and \( R''' \) (around \( x = 3 \)) is \(3-(-6)=9\).

Answer:

1. Rotate figure \( R \) 90° counterclockwise about the origin.
2. Translate the rotated figure up by 6 units.
3. Translate the vertically translated figure to the right by 9 units. (Note: Other valid sequences of three transformations may exist, this is one possible sequence.)