Find the image of P(–2, –1) after two reflections; first Ry=−5(P), and then Rx=1(P1). (1, –5) (–1, –6) (4, –9) (–2, –1)

Answer: third choice (4 - 9).

Explanation:

1) The first reflection, Ry = - 5, means a reflection is across the line y = - 5

2) Since the point P has y-coordinate  - 1, its discance to the line y = - 5 is 4 units (P is located 4 units upper the line y = - 5).

Then, the reflection of the y-coordinate will be 4 units below the line y = - 5, which is -5 - 4 = - 9,

Therefore, the y-coordinate of the image is - 9.

3) The second reflection, Rx = 1, means a reflection across the line x = 1.

4) Since the point P has x-coordinate - 2, its distance to the line x = 1 is 3 units (P is located 3 units to the left of the line x = 1).

Then, the reflection of P will be 3 units to the right of the line x = 1.

That is 1 + 3 = 4.

Therefore, the x-coordinate of the image is 4.

5) You have obtained the x and y - coordinates of the image, x = 4 and y = -9, that is (4, - 9) which is the third choice.