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Given R(x, y) = (-y,x), T (x, y) = (x +1, y + 1), and P(5, -1), what is R (T (P))

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(0,6)

1) Since the notation for transformation is read from right to the left. Let's begin with a Translation over that Point.

2) Translation 1 unit to the right, and 1 unit up:

T (x, y) = (x +1, y + 1)

Pre-image | Rule: | Image

P(5,-1) (x +1, y + 1) P' (6,0)

The next transformation is a Reflection. We can see that according to this rule: r(x, y) = (-y,x) this is a Reflection:

Pre-image | Rule: | Image

P(6,0) (-y,x) P" (0,6)

3) Thus the answer is P"(0,6)

User Joe Mabel
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