Is ΔP’Q’R’ a 180° counterclockwise rotation about the origin of ΔPQR? Explain.
Choose… . The coordinates of the image and preimage Choose… opposites.
Is ΔP’Q’R’ a 180° counterclockwise rotation about the origin of ΔPQR? Explain. The coordinates of the image and preimage opposites.
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To determine if ΔP’Q’R’ is a 180° counterclockwise rotation of ΔPQR about the origin, we need to analyze the coordinates of the points before and after the transformation.
When a point (x, y) is rotated 180° counterclockwise around the origin, its new coordinates become (-x, -y).
So, if we have:
– P(x₁, y₁) becomes P'(-x₁, -y₁)
– Q(x₂, y₂) becomes Q'(-x₂, -y₂)
– R(x₃, y₃) becomes R'(-x₃, -y₃)
If the coordinates of P’, Q’, and R’ match these transformations exactly, then ΔP’Q’R’ is indeed a 180° rotation of ΔPQR about the origin.
In summary, yes, ΔP’Q’R’ is a 180° counterclockwise rotation about the origin of ΔPQR if the coordinates of the image points are the opposites of the preimage points. If you need more assistance on this topic or related concepts, feel free to ask!
To determine if ΔP’Q’R’ is a 180° counterclockwise rotation about the origin of ΔPQR, we need to check the relationship between the coordinates of the points.
If a point (x, y) rotates 180° counterclockwise around the origin, its new coordinates become (-x, -y). This means that the coordinates of the image (P’, Q’, R’) should be the opposites of the corresponding preimage coordinates (P, Q, R).
For example, if you have a point P with coordinates (x, y), after a 180° rotation, the new coordinates P’ will be (-x, -y).
To confirm that ΔP’Q’R’ is indeed a 180° rotation of ΔPQR, you should verify that each point P’, Q’, and R’ corresponds correctly to P, Q, and R as described.
If the coordinates match this transformation, then you can conclude that ΔP’Q’R’ is a 180° counterclockwise rotation of ΔPQR. If not, then it is not.
If you need further clarification or have specific coordinates to evaluate, feel free to ask!