Question

maria determined that △abc is congruent with △abc because it was rotated 270° (counterclockwise). do you agree with every part of marias conclusion? statement #1: yes. △abc was rotated 270° (counterclockwise) and is congruent with △abc. statement #2: no. △abc is congruent with △abc, but it was rotated 90° (counterclockwise), not 270°. statement #3: no. △abc was rotated -90° (clockwise) and is not congruent with △abc.

Explanation:

Step1: Recall rotation rules

A 90 - degree counter - clockwise rotation of a point $(x,y)$ about the origin gives $(-y,x)$. A 270 - degree counter - clockwise rotation of a point $(x,y)$ about the origin gives $(y, - x)$.

Step2: Check rotation of a point

Let's take point $A(3,2)$. A 90 - degree counter - clockwise rotation of $A$ gives $A'(-2,3)$. A 270 - degree counter - clockwise rotation of $A$ gives $A'(2,-3)$. Looking at the graph, if we consider the transformation of point $A$ to $A'$, the transformation is a 90 - degree counter - clockwise rotation. Also, rotation is a rigid transformation which preserves congruence, so $\triangle ABC\cong\triangle A'B'C'$.

Answer:

B. No. $\triangle ABC$ is congruent with $\triangle A'B'C'$, but it was rotated 90° (counterclockwise), not 270°