Find the image of p(3, –1) after two reflections; first ry=-3(p), and then rx=-3(p') a. (3, –1) b. (0, –4) c. (–9, –5) d. (–3, –3)

option C. ( -9, - 5)

Explanation:

1) First reflection.

Reflection across the line y = - 3

This reflection keeps the x-coordinate,which is 3, and changes the y-coordinate to:
y' = -3 - | -3 - (-1) } = - [ - 3 + 1] = - 3 - | -2| = - 3 - 2 - 5

So, p' is (3,- 5)

2) Second reflection.

Reflection accross the line x = - 3 .

This reflection keeps the y coordinate, which is - 5, and changes the x-coordinate to:

x'' = - 3 - |3 - ( - 3) | = - 3 - | -6| =- 3 - 6 = - 9

Then, the final image is (- 9, - 5)