Question

show what you know! a triangle is rotated 90 degrees clockwise about the origin. which coordinate rule describes this transformation? (x,y)→(−x,−y) (x,y)→(y,−x) (x,y)→(x,−y) (x,y)→(−y,x)

Explanation:

Step1: Recall rotation rules

Rotation of a point \((x,y)\) \(90^{\circ}\) clockwise about the origin:
Let's consider a general point \((x,y)\).
When we rotate a point \((x,y)\) \(90^{\circ}\) clockwise, we can use the following geometric reasoning.
The original point \((x,y)\) in the coordinate plane. After a \(90^{\circ}\) clockwise rotation:
The \(x\) - coordinate of the original point becomes the negative of the \(y\) - coordinate of the new point and the \(y\) - coordinate of the original point becomes the \(x\) - coordinate of the new point.
If we start with a point \((x,y)\), after \(90^{\circ}\) clockwise rotation, the new point \((x',y')\) is given by the transformation \((x,y)\to(y, - x)\)

Answer:

\((x,y)\to(y, - x)\)