Question

Find the image of O(-2, -1) after two reflections, first across the line y=-4 and then across the line x= 1
1 (4, -9)
2 (-2, -7)
3 (4, -7)
4 (-2, -9)

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, we can first find the image after the reflection across y=-4.

The distance of point O to the line y=-4 is 3 units, so the image of point O after reflecting across y=-4 will also be 3 units away from the line. Since point O is above the line y=-4, the image will be below the line.

The new y-coordinate will be -4 - 3 = -7. The x-coordinate will remain the same.

After the first reflection, the new point will be O'(-2, -7).

Now, we need to reflect O'(-2, -7) across the line x=1.

The distance of point O' to the line x=1 is 3 units, so the image of point O' after reflecting across x=1 will also be 3 units away from the line. Since point O' is to the left of the line x=1, the image will be to the right.

The new x-coordinate will be 1 + 3 = 4. The y-coordinate will remain the same.

After the second reflection, the final image will be at (4, -7).

Therefore, the correct answer is 3) (4, -7).