Find the image of O (-2,-1) after two reflections, first across the line y=-5, and then across the line x=1.
I believe the answer should be (-1,-6)
Can someone please confirm?
Nope.
Reflecting across the line y = -5 means that the image is as far below the line as (-2,-1) is above it: 4 units. So,
(-2,-1) -> (-2,-9)
Same with the line x=1. 3 to the left, so 3 to the right.
(-2,-9) -> (4,-9)
Reflecting across the line y=k:
(x,y) -> (x,k-(y-k))
Across the line x-h:
(x,y) -> (h-(x-h),y)
So, the two reflections take
(x,y) -> (h-(x-h),k-(y-k))
In this case,
(-2,-1) -> (1-(-2-1),-5-(-1+5)) = (4,-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, follow these steps:
1. Reflection across y = -5:
- The line of reflection, y = -5, is a horizontal line.
- The distance between O and the line of reflection is 4 units (from -1 to -5).
- To reflect a point across a horizontal line, you need to change the sign of the y-coordinate and keep the x-coordinate the same.
- So, reflecting O across y = -5 gives us the point O' (-2, -9).
2. Reflection across x = 1:
- The line of reflection, x = 1, is a vertical line.
- The distance between O' and the line of reflection is 3 units (from -2 to 1).
- To reflect a point across a vertical line, you need to change the sign of the x-coordinate and keep the y-coordinate the same.
- So, reflecting O' across x = 1 gives us the final point O'' (1, -9).
Therefore, the image of O (-2, -1) after two reflections is O'' (1, -9), not (-1, -6).