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Suppose ΔPQR is rotated 270° about the origin, (0,0). Find the coordinates of P′, Q′, and R′. Then sketch ΔP′Q′R′.

Suppose ΔPQR is rotated 270° about the origin, (0,0). Find the coordinates of P′, Q-example-1
User Kgdesouz
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1 Answer

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In case it is a 270º Counter-clockwise rotation:

P'(3,-3), Q'(5,-5), R'(6,-3)

In case it is a 270º Clockwise rotation:

P'(-3, 3), Q'(-5,5), R'(-6,3)

1) Since in this case, there is a 270º rotation about the origin then we can write out the following:

As there is no mention of the direction then we'll do it for both cases.

2) For a 270º Counter-Clockwise rotation

Pre-image rule Image

P(3,3) (x,y)=(y,-x) P'(3,-3)

Q(5,5) Q'(5,-5)

R(3,6) R'(6,-3)

3) For a Clockwise Direction

Pre-image rule Image

P(3,3) (x,y)=(-y,x) P'(-3, 3)

Q(5,5) Q'(-5,5)

R(3,6) R'(-6,3)

Suppose ΔPQR is rotated 270° about the origin, (0,0). Find the coordinates of P′, Q-example-1
Suppose ΔPQR is rotated 270° about the origin, (0,0). Find the coordinates of P′, Q-example-2
User ChristianCuevas
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