find the image of O(-2,-1) after 2 reflections, first across the line y=-4 and then across the line x=1
First reflection across y = -4:
The image of point O after reflecting across the line y = -4 will be O'(x, y') with the same x-coordinate as O but a y-coordinate that is calculated as follows:
y' = 2*(-4) - (-1) = -8 + 1 = -7
Therefore, the image of O after the first reflection is O'(x, -7).
Second reflection across x = 1:
The image of point O' after reflecting across the line x = 1 will be O''(x', y'') with the same y-coordinate as O' but an x-coordinate that is calculated as follows:
x' = 2*1 - (-2) = 2 + 2 = 4
Therefore, the final image of O after both reflections is O''(4, -7).