If point (p 4, 11) is reflected
across the line y = 3, what are
the coordinates of its reflection
image?
The line y = 3 is the horizontal line that intersects the y-axis at 3.
To reflect point (4, 11) across the line y = 3, we need to find the distance between the point and the line and then reflect it to the other side of the line by the same distance.
The distance between point (4, 11) and the line y = 3 is 11 - 3 = 8 units.
Since the line is horizontal, the y-coordinate of the reflection image will remain the same at 11.
To find the x-coordinate of the reflection image, we need to move 8 units in the opposite direction, since the line is below the point.
So, the x-coordinate of the reflection image will be 4, but reflected across y = 3, it will be 4 units to the left of the line.
Therefore, the coordinates of the reflection image are (-4, 11).
you sure?
Apologies for the mistake in my previous response.
To reflect a point across a horizontal line, we keep the y-coordinate the same and find the difference between the y-coordinate of the point and the equation of the line to get the vertical distance from the line. Then, we add this distance to the y-coordinate to get the new y-coordinate.
Given:
- Point (4, 11)
- Equation of the line: y = 3
The vertical distance from the point to the line is |11 - 3| = 8.
Since the line y = 3 is below the point, we subtract this distance from y = 3, which gives us:
3 - 8 = -5
Therefore, the coordinates of the reflection image are (4, -5).