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Rotations Quick Check 5 of 55 of 5 Items Question Use the image to answer the question. Imagine a counterclockwise rotation of 270° about the origin of the figure. Choose the coordinate of A′ . (1 point) Responses (1,1) left parenthesis 1 comma 1 right parenthesis (2,−1) left parenthesis 2 comma negative 1 right parenthesis (−1,−2) left parenthesis negative 1 comma negative 2 right parenthesis (1,2) left parenthesis 1 comma 2 right parenthesis Skip to navigation page 16 of 16 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.
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GPT-4o mini
To find the coordinates of \( A' \) after a counterclockwise rotation of 270° around the origin, we can apply the rotation transformation formulas.
For a point \( (x, y) \), the formulas for a counterclockwise rotation are:
- A 90° rotation maps \( (x, y) \) to \( (-y, x) \).
- A 180° rotation maps \( (x, y) \) to \( (-x, -y) \).
- A 270° (which is equivalent to a -90°) rotation maps \( (x, y) \) to \( (y, -x) \).
If we denote the original coordinates of point \( A \) as \( (x, y) \), then after a 270° counterclockwise rotation, the new coordinates \( A' \) will be:
\[
A' = (y, -x)
\]
Please provide the coordinates of point \( A \) so I can calculate \( A' \). Without those coordinates, it's not possible to determine the specific new position.
For a point \( (x, y) \), the formulas for a counterclockwise rotation are:
- A 90° rotation maps \( (x, y) \) to \( (-y, x) \).
- A 180° rotation maps \( (x, y) \) to \( (-x, -y) \).
- A 270° (which is equivalent to a -90°) rotation maps \( (x, y) \) to \( (y, -x) \).
If we denote the original coordinates of point \( A \) as \( (x, y) \), then after a 270° counterclockwise rotation, the new coordinates \( A' \) will be:
\[
A' = (y, -x)
\]
Please provide the coordinates of point \( A \) so I can calculate \( A' \). Without those coordinates, it's not possible to determine the specific new position.
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