Answer:
- 2 units left
- 2 units down
- reflection across the y-axis
Step-by-step explanation:
The letters designating the original figure, RSTU, start at the bottom of the figure and proceed clockwise around it. The letters designating the image, R'S'T'U' start at the bottom and proceed counterclockwise around it. This tells you ...
- the figure has been reflected once (CW-CCW order is reversed)
- the line of reflection is a vertical line (up-down orientation hasn't changed)
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The fill-in for the answer tells you that translation takes place before reflection. To figure out how much translation is needed, you need to know the line of reflection.
Line of Reflection
You can look at the reflection choices to see where the line of reflection is. We're guessing that the only vertical line choice is the y-axis. (If the line of reflection is x=1, there doesn't need to be any horizontal translation.) If the image is reflected across the y-axis, the point R' moves from (-3, 0) to (3, 0). This is where R' is reflected from.
Translation
The point R is at (5, 2). To move R from (5, 2) to (3, 0) prior to reflection, the x-coordinate needs to decrease by 2 (from 5 to 3), and the y-coordinate also needs to decrease by 2 (from 3 to 0). That is, the point R must be translated left 2 and down 2 to get it to (3, 0).
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R'S'T'U' is the image of RSTU after translation 2 left, 2 down, and reflection across the y-axis.
