Question

triangle c is rotated 270° counterclockwise with the origin as the center of rotation to create a new figure. which triangle shows the new location?

Explanation:

Step1: Recall rotation rule

A $270^{\circ}$ counter - clockwise rotation about the origin is equivalent to a $90^{\circ}$ clockwise rotation. The rule for a $90^{\circ}$ clockwise rotation of a point $(x,y)$ about the origin is $(x,y)\to(y, - x)$.

Step2: Analyze the orientation

When we rotate a triangle $270^{\circ}$ counter - clockwise (or $90^{\circ}$ clockwise) about the origin, the orientation of the triangle changes. We can also think of it in terms of the quadrants. Triangle C is in the fourth quadrant. After a $270^{\circ}$ counter - clockwise rotation, it will move to the first quadrant.

Step3: Identify the new location

By observing the given triangles, triangle B is in the first - quadrant and has the correct orientation after the rotation of triangle C about the origin.

Answer:

B. Option Text