Question

which rotation is shown in the coordinate plane? 90° counterclockwise 180° counterclockwise 90° clockwise 180° clockwise

Explanation:

Step1: Recall rotation rules

For a \(90^{\circ}\) clockwise rotation \((x,y)\to(y, -x)\), for \(180^{\circ}\) rotation \((x,y)\to(-x,-y)\), for \(90^{\circ}\) counter - clockwise rotation \((x,y)\to(-y,x)\).

Step2: Assume a point

Let's take point \(B\). Suppose \(B\) has coordinates \((-1, -1)\). After rotation, \(B'\) has coordinates \((1, -1)\).
If we consider \(90^{\circ}\) clockwise rotation:
Let the original point be \((x,y)\). Using the formula \((x,y)\to(y, -x)\). If \(x=-1,y = - 1\), then \((y,-x)=(-1,1)\) (not correct).
For \(180^{\circ}\) rotation \((x,y)\to(-x,-y)\), if \(x=-1,y=-1\), then \((-x,-y)=(1,1)\) (not correct).
For \(90^{\circ}\) counter - clockwise rotation \((x,y)\to(-y,x)\), if \(x = - 1,y=-1\), then \((-y,x)=(1,-1)\) (correct).

Answer:

\(90^{\circ}\) counterclockwise