Find the image of O(-2,-1) after two reflections, first across the line y=-4 and then across the line x = 1
To find the image of point O(-2,-1) after two reflections, first across the line y=-4 and then across the line x=1, we need to perform the reflections one after the other.
1. Reflection across y=-4:
To reflect a point across a horizontal line, we only need to change the sign of the y-coordinate while keeping the x-coordinate the same.
So, the image of O(-2,-1) after the first reflection is O'(-2,5).
2. Reflection across x=1:
To reflect a point across a vertical line, we only need to change the sign of the x-coordinate while keeping the y-coordinate the same.
So, the image of O'(-2,5) after the second reflection is O''(2,5).
Therefore, the final image of O(-2,-1) after two reflections, first across the line y=-4 and then across the line x=1, is O''(2,5).