Find the image of O(-2,-1) after two reflections, first across the line y=-4 and then across the line x = 1(1 point)

Answer 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, you will perform the following steps:

1. Reflect point O(-2, -1) across the line y = -4:
The distance between point O and the line y = -4 is 3 units (4 - 1 = 3). Since point O is 3 units above the line y = -4, its reflection will be 3 units below the line. Therefore, the image of point O after the first reflection is O'(-2, -7).

2. Reflect point O'(-2, -7) across the line x = 1:
The distance between point O' and the line x = 1 is 3 units (1 - (-2) = 3). Since point O' is 3 units to the left of the line x = 1, its reflection will be 3 units to the right of the line. Therefore, the final image of point O after the second reflection is O''(5, -7).

Therefore, the image of point O(-2, -1) after the two reflections is O''(5, -7).