Question

the diagram shows a right triangle. if the triangle is rotated 90° counterclockwise about the origin, what will the image be?

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree counter - clockwise rotation about the origin for a point $(x,y)$ is $(-y,x)$. For a triangle, we apply this rule to each of its vertices.

Step2: Visualize the rotation

When a right - triangle in the first quadrant (assuming the given triangle is in a standard position) is rotated 90 degrees counter - clockwise about the origin, it will move to the second quadrant. The orientation of the right - angle will change accordingly.

Answer:

The triangle will be in the second quadrant with its sides perpendicular to the original sides and the right - angle vertex at the origin (if the original right - angle vertex was at the origin before rotation). The new triangle is obtained by applying the transformation $(x,y)\to(-y,x)$ to each vertex of the original triangle.