Question

The square, with vertices A, B, C, and D, appears centered on the Cartesian plane.

After rotating 90 degrees clockwise about the origin:

Original Point A (-2, 1) moves to Point A’ (1, 2)

Original Point B (1, 1) moves to Point B’ (1, -2)

Original Point C (1, -1) moves to Point C’ (-2, -1)

Original Point D (-2, -1) moves to Point D’ (-1, 2)

On a rotated coordinate plane, the new quadrilateral might lie within a creative mirrored flipped portion .
Imagine a counterclockwise rotation of 270°
about the origin of the figure. Choose the coordinate of A′
.

(1 point)
Responses

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

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

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

(−1,−2)

Answer 1

To find the coordinates of point A' after a 270-degree counterclockwise rotation about the origin, we can use the transformation rule for such a rotation.

The transformation for a point (x, y) after a 270-degree counterclockwise rotation is given by the formula:
\[
(x, y) \to (y, -x)
\]

Given that point A' is located at (1, 2), we will apply the transformation to this point:

1. Take the x-coordinate (1) and the y-coordinate (2).
2. Apply the transformation:
- New x-coordinate: y = 2
- New y-coordinate: -x = -1

Thus, the new coordinates after a 270-degree counterclockwise rotation about the origin will be:
\[
(2, -1)
\]

So, the correct answer is \( (2, -1) \).