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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 (1,2) left parenthesis 1 comma 2 right parenthesis (2,−1) left parenthesis 2 comma negative 1 right parenthesis (−1,−2)

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To find the coordinates of the point A′ that results from a 270° counterclockwise rotation about the origin, we can use the rotation formula for points in the Cartesian coordinate system.

The general rule for a 270° counterclockwise rotation (or equivalently a 90° clockwise rotation) of a point (x, y) around the origin is given by the following transformation:

\[ (x, y) \rightarrow (y, -x) \]

Let's consider the given options for point A. However, you didn't provide the original coordinates of point A (before rotation).

If we assume that the original coordinates of point A are one of the options provided, we can apply the rotation transformation:

  1. If A = (1, 1) then A′ = (1, -1).
  2. If A = (1, 2) then A′ = (2, -1).
  3. If A = (2, -1) then A′ = (-1, -2).
  4. If A = (-1, -2) then A′ = (-2, 1).

Matching the options you provided, the correct transformation will yield the following results:

  1. From (1, 1) ⇒ (1, -1) – Not available.
  2. From (1, 2) ⇒ (2, -1) – Present in options.
  3. From (2, -1) ⇒ (-1, -2) – Present in options.
  4. From (-1, -2) ⇒ (-2, 1) – Not available.

Since the question did not provide specific original coordinates for point A, we can conclude that if we assume the original point A was (1, 2), then after a 270° rotation, A′ would be (2, -1).

Therefore, the response corresponding to the correct transformed point A′ is:

(2, -1)