Question

4.1 engage: grid transformations
due on 10.30.2025 10 total points 2 total attempts
answer the question correctly to continue:
point ( p ( 2,3 ) ) is rotated ( 90 ^ { circ } ) counterclockwise around the origin.
which statement best explains what happens to the coordinates?
the coordinate s switch places, and the
both coordinate s change signs
only the ( y - ) coordinate changes sign
the coordinate s stay the same because

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(90^{\circ}\) counter - clockwise around the origin, the new coordinates \((x',y')\) are given by the transformation \((x,y)\to(-y,x)\).
For the point \(P(2,3)\), \(x = 2\) and \(y=3\). After rotation, the new \(x'\) coordinate is \(-y=-3\) and the new \(y'\) coordinate is \(x = 2\).

Step2: Analyze the transformation of coordinates

The original coordinates \((2,3)\) become \((-3,2)\). The \(x\) and \(y\) coordinates switch places (\(x = 2\) and \(y = 3\) become \(x'=-3\) (from \(-y\)) and \(y'=2\) (from \(x\))).

Answer:

The coordinate s switch places, and the