describe a sequence of transformations for which quadrilateral p is the image of quadrilateral q.

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.