Is ΔP’Q’R’ a 180° counterclockwise rotation about the origin of ΔPQR? Explain.
No
The coordinates of the image and preimage are
opposites.
Is ΔP’Q’R’ a 180° counterclockwise rotation about the origin of ΔPQR? Explain
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Is ΔP’Q’R’ a 180° counterclockwise rotation about the origin of ΔPQR? Explain.
No
The coordinates of the image and preimage are
opposites.
Yes, ΔP’Q’R’ is a 180° counterclockwise rotation about the origin of ΔPQR.
When a figure is rotated 180° around the origin, the coordinates of each point change as follows: If a point has coordinates (x, y), after a 180° rotation, its new coordinates will be (-x, -y). This means that each vertex of the rotated triangle will have opposite coordinates to those in the original triangle, confirming that the coordinates of the image and preimage are indeed opposites.
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To determine if ΔP’Q’R’ is a 180° counterclockwise rotation of ΔPQR about the origin, we can specifically look at how the coordinates change during such a rotation.
For a 180° rotation about the origin, the transformation of a point (x, y) is given by:
[ (x, y) rightarrow (-x, -y) ]
This means that for every point in ΔPQR, the corresponding point in ΔP’Q’R’ would have coordinates that are the negatives of the original coordinates.
If the coordinates of the image (ΔP’Q’R’) are indeed opposites of the original coordinates (ΔPQR), then the answer is yes; ΔP’Q’R’ is indeed the result of a 180° counterclockwise rotation of ΔPQR about the origin.
In summary, if ΔP’Q’R’ consists of points that are the negatives of the points in ΔPQR, then ΔP’Q’R’ is a 180° rotation of ΔPQR.