Answer:
- rotation 90° CW about the origin
- translation up 5 units
Explanation:
You want a transformation that maps figure P in the 3rd quadrant to figure Q in the second quadrant.
Rotation
The figures have the same orientation (sequence of angles and side lengths), so reflection is not needed as part of the transformation.
The shorter mid-length side in Figure P has a slope of -1, and the corresponding side in Figure Q has a slope of +1. This can be the result of a 90° clockwise rotation about the origin.
Rotation 90° CW about the origin will map the right-angle corner from (-7, -7) to (-7, 7).
Translation
The right-angle corner in Figure Q is at (-7, 12), so a translation upward after the rotation is required. The amount of that translation is 12-7 = 5 units.
Translation upward by 5 units will map the right angle corner from its rotated position at (-7, 7) to its position in Figure Q at (-7, 12).
The series of transformations could be ...
- Rotation 90° CW about the origin
- Translation up by 5 units
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Additional comment
The required transformation can be accomplished in one step by rotation 90° CW about the point (2.5, 2.5).
If Figure P is rotated 90° CW about its right-angle corner, then translation up by 19 units will map it to Figure Q. That is, there are many combinations of rotation and translation that will do the job.