9514 1404 393
Answer:
- Rotate Q 90° CCW to make Q'
- Translate Q' down 6 units to make P
or
- Translate Q left 6 units to make P'
- Rotate P' 90° CCW to make P
Step-by-step explanation:
The orientation of image P is apparently 90° counterclockwise from the orientation of Q. Hence one of the required transformations is a 90° CCW rotation. A suitable choice of the center of rotation would make that be the only required transformation.
If we choose the origin as the center of rotation, we can map figure Q to image P either of a couple of ways:
1. translate the figure 6 units left then rotate 90° CCW
2. rotate the figure 90° CCW, then translate 6 units down.
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Rotation 90° CCW is accomplished by the transformation ...
(x, y) ⇒ (-y, x)
Translation 6 units down is described by ...
(x, y) ⇒ (x, y -6)
Then the composition of these transformations (90° CCW, followed by 6 down) will be ...
(x, y) ⇒ (-y, x -6)
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Alternatively, we can translate left 6 units first, then do the rotation:
(x, y) ⇒ (x -6, y) . . . . . . . translate 6 left
(x, y) ⇒ (-y, x -6) . . . . . . rotate the translated figure 90° CCW
You will notice that the composition of transformations has the same description regardless of the order.
