Question

midterm cumulative test
the graph of △rst is shown.
the triangle is rotated 90° counterclockwise about the origin to create △rst. what are the
o (-8,4)
o (8,-4)
o (4,-8)
o (-4,8)

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: Apply the rule

Since no specific point is given in the question text (but assuming we are working with a general point in the triangle), if we have a point $(x,y)$ and rotate it 90 degrees counter - clockwise about the origin, the new coordinates will follow the above rule. Without seeing the actual coordinates of the points in $\triangle RST$ in the figure clearly, for a general point, if we assume a point $(8,4)$ (as an example of a point in the original triangle), after a 90 - degree counter - clockwise rotation about the origin, using the rule $(x,y)\to(-y,x)$, the new point will be $(-4,8)$.

Answer:

If we assume the original point is $(8,4)$ (as an example), the rotated point is $(-4,8)$. But since the question seems incomplete without clear original coordinates of a point in the triangle, the general rule for a 90 - degree counter - clockwise rotation about the origin $(x,y)\to(-y,x)$ is key.