What is the image of A(3,-1) after a reflection, first across the line y=3, and then across the line x=-1?
I believe (3,-1) but not real sure, doesn't the x stay the same?
i hate math
(x,y) -> (x,6-y)
then
(x,y) -> (-1-(x+1),y) = (-2-x,y)
so, (x,y) -> (x,6-y) -> (-2-x,6-y)
(3,-1) -> (3,7) -> (-5,7)
thanxx Steve very much ;)
To find the image of a point after a sequence of reflections, you can follow these steps:
1. Reflect the point across the first line:
- In this case, the line y = 3 is a horizontal line parallel to the x-axis.
- To reflect the point A(3, -1) across this line, we need to keep the x-coordinate the same and reflect the y-coordinate.
- Since the line y = 3 is 3 units above the x-axis, the new y-coordinate will be 3 units below the x-axis.
- Therefore, after reflecting across y = 3, the new coordinates will be A(3, -5).
2. Reflect the new point across the second line:
- The line x = -1 is a vertical line parallel to the y-axis.
- To reflect the point A(3, -5) across this line, we need to keep the y-coordinate the same and reflect the x-coordinate.
- Since the line x = -1 is 1 unit to the left of the y-axis, the new x-coordinate will be 1 unit to the right of the y-axis.
- Therefore, after reflecting across x = -1, the final image of point A is A(2, -5).
So, the image of point A(3, -1) after the sequence of reflections is A(2, -5).