Question

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

Explanation:

Step1: Recall rotation rules

For a point \((x,y)\) rotated \(180^{\circ}\) counter - clockwise or clockwise about the origin, the new coordinates are \((-x,-y)\). For a \(90^{\circ}\) counter - clockwise rotation, the new coordinates are \((-y,x)\) and for a \(90^{\circ}\) clockwise rotation, the new coordinates are \((y, - x)\).

Step2: Analyze a point

Let's take point \(D\). Suppose \(D=(1,-2)\). After rotation, \(D'=(-1,2)\). If we use the \(180^{\circ}\) rotation formula \((x,y)\to(-x,-y)\), for \(x = 1\) and \(y=-2\), we get \((-1,2)\).

Answer:

\(180^{\circ}\) counterclockwise, \(180^{\circ}\) clockwise