Question

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

Explanation:

Step1: Recall rotation rules

• 90° counter - clockwise rotation: $(x,y)\to(-y,x)$
• 90° clockwise rotation: $(x,y)\to(y, - x)$
• 180° rotation (clockwise or counter - clockwise): $(x,y)\to(-x,-y)$

Step2: Assume a point

Let's take a point from the original triangle. Suppose in triangle \(DEF\), take point \(D\). Assume \(D=(3, - 1)\) (from the coordinate plane). After rotation, its image \(D'=(-3,1)\)

Step3: Apply rotation rules

Using the 180° rotation rule \((x,y)\to(-x,-y)\), for \(x = 3\) and \(y=-1\), we get \((-3,1)\)

Answer:

180° counterclockwise (since 180° clockwise and 180° counter - clockwise give the same result for point rotation \((x,y)\to(-x,-y)\) in terms of the final position of the figure in the coordinate plane)