Question

Find the image of O(–2, –1) after two reflections, first across the line y = –5, and then across the line x = 1.
(1 point)
Responses

(–2, –1)
(–2, –1)

(–1, –6)
(–1, –6)

(4, –9)
(4, –9)

(1, –5)

Answer 1

To find the image of a point after two reflections, we can combine the transformations by finding the composition of the two reflection matrices.

First reflection across the line y = -5:

Let's reflect the point O(-2, -1) across the line y = -5.

The line y = -5 is a horizontal line, and reflecting a point across a horizontal line involves changing the sign of the y-coordinate while keeping the x-coordinate the same.

So the image of O(-2, -1) after the first reflection across y = -5 is O(-2, -9).

Second reflection across the line x = 1:

Now, let's reflect the point O(-2, -9) across the line x = 1.

The line x = 1 is a vertical line, and reflecting a point across a vertical line involves changing the sign of the x-coordinate while keeping the y-coordinate the same.

So the image of O(-2, -9) after the second reflection across x = 1 is O(2, -9).

Therefore, the final image of O(-2, -1) after the two reflections is (2, -9).