What is the image of A(3, –1) after a reflection, first across the line y = 3, and then across the line x = –1?
(1 point)
Responses
(–5, 7)
(–5, 7)
(3, –1)
(3, –1)
(–5, –1)
(–5, –1)
(1, –5)
To find the image of A(3, -1) after a reflection across the line y = 3, we need to reflect point A over the line y = 3.
The line y = 3 is a horizontal line passing through the y-coordinate 3. Since the line is horizontal, the x-coordinate remains the same and only the y-coordinate changes.
So the reflection of A(3, -1) across the line y = 3 will result in the point (3, 5).
Now, to find the image of (3, 5) after a reflection across the line x = -1, we need to reflect the point over the vertical line x = -1.
The line x = -1 is a vertical line passing through the x-coordinate -1. Since the line is vertical, the y-coordinate remains the same and only the x-coordinate changes.
So the reflection of (3, 5) across the line x = -1 will result in the point (-5, 5).
Therefore, the image of A(3, -1) after a reflection first across the line y = 3, and then across the line x = -1 is: (-5, 5).
To find the image of point A(3, -1) after a reflection, first across the line y = 3, and then across the line x = -1, follow these steps:
Step 1: Reflect across the line y = 3:
- Draw a line parallel to the y-axis passing through the given point A(3, -1).
- Measure the perpendicular distance between this line and the line y = 3.
- This perpendicular distance will be the same on both sides of the line y = 3.
- Reflect the point A across the line y = 3 by moving it the same distance on the other side of the line.
- The reflected point is A'(3, 5).
Step 2: Reflect across the line x = -1:
- Draw a line parallel to the x-axis passing through the previously reflected point A'(3, 5).
- Measure the perpendicular distance between this line and the line x = -1.
- This perpendicular distance will be the same on both sides of the line x = -1.
- Reflect the point A' across the line x = -1 by moving it the same distance on the other side of the line.
- The final image point is A''(-5, 5).
Therefore, the image of A(3, -1) after a reflection across the line y = 3 and then across the line x = -1 is (-5, 5).
Note: The given options do not match the correct answer. The correct answer is (-5, 5), not (–5, 7), (3, –1), (–5, –1), or (1, –5).