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)
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).
To find the image of point O(-2, -1) after two reflections, first across the line y = -5 and then across the line x = 1, we can follow these steps:
1. Reflecting across the line y = -5:
- In this case, the y-coordinate of the point O remains unchanged, since it lies on the line of reflection.
- To find the new x-coordinate, we can calculate the distance between the original point and the line y = -5, which is 5 units.
- Since the original x-coordinate is -2, the new x-coordinate will be -2 + 2(5) = 8.
2. Reflecting across the line x = 1:
- In this case, the x-coordinate of the point remains unchanged, since it lies on the line of reflection.
- To find the new y-coordinate, we can calculate the distance between the previous image point (-2, -1) and the line x = 1, which is 3 units below the line.
- Since the previous y-coordinate is -1, the new y-coordinate will be -1 + 2(3) = 5.
So, the image of point O(-2, -1) after the two reflections is (8, 5).
Therefore, the correct response is:
(8, 5)