Question

What is the reflection image of P(0, 0) after two reflections, first across x = 4 and then across y = -3?

A) (8, -6)
B) (8, -3)
C) (8, 6)
D) (4, -3)

Answer 1

The reflection image of the point P(0, 0) after reflecting across x = 4 and then across y = -3, is located at (8, -6).

Step-by-step explanation:

The student is asking about the reflection of a point P(0, 0) after two reflections - first across the vertical line x = 4, and then across the horizontal line y = -3. To solve this, we reflect the point P over the two lines step by step.

First, reflecting across x = 4 implies that the point will move horizontally to the other side of the line x = 4, at an equal distance. Since P is 4 units away from this line, after the reflection, it will be at (8, 0).

Next, reflecting this new point across y = -3 means that the point will now move vertically to the other side of the line y = -3, again at an equal distance. Since our new point is 3 units away from this line, after this reflection, the final position will be at (8, -6).

Therefore, after these two reflections, the final position of the reflected point is (8, -6), corresponding to option A.