Question

1. a point is rotated 90 degrees clockwise around a non-origin point (1, 1). what must be done after applying the rotation?

a. translate the figure back to its original position relative to (1, 1)
b. reflect the point over the y-axis
c. negate the coordinates of the rotated point
d. swap the coordinates again

Explanation:

Step1: Recall rotation about non-origin

To rotate a point $(x,y)$ 90° clockwise about $(h,k)$: first translate the point so $(h,k)$ becomes the origin: $(x-h, y-k)$.

Step2: Apply 90° clockwise rotation

The 90° clockwise rotation rule about origin is $(a,b) \to (b, -a)$. So translated point becomes $(y-k, -(x-h))$.

Step3: Translate back to original plane

To get the final rotated point relative to the original coordinate system, add back $(h,k)$: $(y-k+h, -(x-h)+k)$. This step is translating the figure back to its original position relative to $(1,1)$.

Answer:

a. Translate the figure back to its original position relative to (1,1)