Question

name amolun smith for exercise 12, select the best answer. 12. which of the following statements describes the rotation shown? (lesson 3) a. 90° counterclockwise rotation b. 180° clockwise rotation c. 270° clockwise rotation d. 360° counterclockwise rotation

Explanation:

Step1: Recall rotation rules

A 90 - degree counter - clockwise rotation of a point $(x,y)$ about the origin results in the point $(-y,x)$. A 180 - degree clockwise (or counter - clockwise) rotation of a point $(x,y)$ about the origin results in the point $(-x,-y)$. A 270 - degree clockwise rotation of a point $(x,y)$ about the origin is the same as a 90 - degree counter - clockwise rotation, resulting in $(-y,x)$. A 360 - degree rotation of a point $(x,y)$ about the origin results in the point $(x,y)$ itself.

Step2: Analyze the given triangles

Let's take a point, say point $A$ in the original triangle $\triangle ABC$. Assume $A=(0, - 2)$. In the rotated triangle $\triangle A'B'C'$, the corresponding point $A'=(2,0)$. When we rotate a point $(x,y)=(0,-2)$ 90 degrees counter - clockwise about the origin, using the rule $(x,y)\to(-y,x)$, we get $-(-2)=2$ and $x = 0$ becomes $y = 0$, so the new point is $(2,0)$.

Answer:

A. 90° counterclockwise rotation