Question

Use the image to answer the question.A quadrilateral is plotted a coordinate plane with both the axes ranging from negative 6 to 6.Imagine a counterclockwise rotation of 270° about the origin of the figure. Choose the coordinate of A′.(1 point)Responses(1,2)left parenthesis 1 comma 2 right parenthesis(−1,−2)left parenthesis negative 1 comma negative 2 right parenthesis(1,1)left parenthesis 1 comma 1 right parenthesis(2,−1)

Answer 1

To find the coordinates of A' after a counterclockwise rotation of 270° about the origin, you can use the rotation transformation formula.

A counterclockwise rotation of 270° is equivalent to a clockwise rotation of 90°. The transformation for rotating a point (x, y) 90° clockwise is given by:

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

Now, let’s apply this transformation to each of the possible original points to see which one matches the options given.

Suppose A has coordinates (1, 2):

1. Applying the transformation: \[ (1, 2) \rightarrow (2, -1) \]

Now, let's check each of the options given for A:

1. (1, 2) → (2, -1) (Matches)
2. (−1, −2) → (−2, 1) (Does not match)
3. (1, 1) → (1, -1) (Does not match)
4. (2, −1) → (−1, -2) (Does not match)

The correct choice for the coordinates of A' after a 270° counterclockwise rotation about the origin is:

\((2, -1)\).