Question
Triangle XYZ is rotated 90° clockwise about the origin.
On a coordinate plane, triangle X Y Z has points (negative 3, 1), (4, 4), (4, 1).
What are the coordinates of point X’?
(1, 3)
(3, –1)
(3, 1)
(–1, –3)
On a coordinate plane, triangle X Y Z has points (negative 3, 1), (4, 4), (4, 1).
What are the coordinates of point X’?
(1, 3)
(3, –1)
(3, 1)
(–1, –3)
Answers
GPT-4o mini
To rotate a point \((x, y)\) 90° clockwise about the origin, you can use the transformation:
\[
(x, y) \rightarrow (y, -x)
\]
Now, let's apply this transformation to point \(X\), which has the coordinates \((-3, 1)\).
Using the formula:
\[
X' = (y, -x) = (1, -(-3)) = (1, 3)
\]
Therefore, the coordinates of point \(X'\) after the rotation are \((1, 3)\).
Among the provided options, the correct answer is \((1, 3)\).
\[
(x, y) \rightarrow (y, -x)
\]
Now, let's apply this transformation to point \(X\), which has the coordinates \((-3, 1)\).
Using the formula:
\[
X' = (y, -x) = (1, -(-3)) = (1, 3)
\]
Therefore, the coordinates of point \(X'\) after the rotation are \((1, 3)\).
Among the provided options, the correct answer is \((1, 3)\).