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′ (-2,1)

(1 point)
Responses

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

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

(1,1)
left parenthesis 1 comma 1 right parenthesis

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

To determine the new coordinates of point A' (-2, 1) after a 270° counterclockwise rotation about the origin, we can use the rotation transformation formula. The standard transformation for a counterclockwise rotation of \(\theta\) degrees is as follows:

For a point \((x, y)\):
- After a \(90^\circ\) rotation, the new coordinates will be \((-y, x)\).
- After a \(180^\circ\) rotation, the new coordinates will be \((-x, -y)\).
- After a \(270^\circ\) rotation, the new coordinates will be \((y, -x)\).

Given the point A' with coordinates (-2, 1):
- Apply the transformation for a \(270^\circ\) counterclockwise rotation:

\[
A' \text{ (before rotation)} = (-2, 1)
\]

By substituting \(x = -2\) and \(y = 1\):
\[
A' \text{ (after rotation)} = (1, -(-2)) = (1, 2)
\]

Therefore, the new coordinates of point A' after a 270° counterclockwise rotation about the origin are \((1, 2)\).

The correct response is **(1, 2)**.