Question
Point A(-2,1) Point B(1,1) Point c(1,-1) Point D(-2,-1)
Imagine a counterclockwise rotation of 270 degree about the origin of the figure. Choose the coordinate of A'.
(1,2)
(1,1)
(-1,-2)
(2,-1)
Imagine a counterclockwise rotation of 270 degree about the origin of the figure. Choose the coordinate of A'.
(1,2)
(1,1)
(-1,-2)
(2,-1)
Answers
Answered by
GPT-4o mini
To find the coordinates of point A after a counterclockwise rotation of 270 degrees about the origin, we can use the formula for rotation in the coordinate plane.
The 270-degree counterclockwise rotation can be thought of as a 90-degree clockwise rotation. The transformation for a point \((x, y)\) under a 90-degree clockwise rotation is given by:
\[
(x, y) \to (y, -x)
\]
So, applying this transformation to point \(A(-2, 1)\):
1. **Identify the coordinates of A**:
\((x, y) = (-2, 1)\)
2. **Apply the transformation**:
\[
A' = (y, -x) = (1, -(-2)) = (1, 2)
\]
Thus, the coordinates of \(A'\) after a 270-degree counterclockwise rotation are \((1, 2)\).
The correct answer is \((1, 2)\).
The 270-degree counterclockwise rotation can be thought of as a 90-degree clockwise rotation. The transformation for a point \((x, y)\) under a 90-degree clockwise rotation is given by:
\[
(x, y) \to (y, -x)
\]
So, applying this transformation to point \(A(-2, 1)\):
1. **Identify the coordinates of A**:
\((x, y) = (-2, 1)\)
2. **Apply the transformation**:
\[
A' = (y, -x) = (1, -(-2)) = (1, 2)
\]
Thus, the coordinates of \(A'\) after a 270-degree counterclockwise rotation are \((1, 2)\).
The correct answer is \((1, 2)\).