Question

17 multiple choice 2 points in the accompanying diagram, △abc is a right triangle. which diagram below represents the image of △abc when rotated 90° counterclockwise about the origin?

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree counter - clockwise rotation about the origin for a point $(x,y)$ is $(x,y)\to(-y,x)$.

Step2: Analyze triangle vertices

Let's assume the vertices of $\triangle ABC$ are $A(x_1,y_1)$, $B(x_2,y_2)$, $C(x_3,y_3)$. After 90 - degree counter - clockwise rotation, the new vertices will be $A'(-y_1,x_1)$, $B'(-y_2,x_2)$, $C'(-y_3,x_3)$. Geometrically, this rotation will move the triangle from the first - quadrant (as shown in the original $\triangle ABC$) to the second quadrant.

Step3: Check options

The original right - triangle has a right - angle at $C$ and is in the first quadrant. After a 90 - degree counter - clockwise rotation about the origin, the right - triangle should be in the second quadrant with the right - angle still present. The correct option is the one where the triangle is in the second quadrant.

Answer:

The third option (where the triangle is in the second quadrant).