Find the image of O(-2, -1) after two reflections, first across the line y = -5 and then across the line x = 1.
(-2, -1)
(-1, -6)
(4, -9)
(1, -5)
I am very confused, no idea what this means. Please help? Thanks
Nevermind, it's 4, -9:) (for certain, just got it)
To find the image of point O(-2, -1) after the two given reflections, you can follow these steps:
1. Reflect the point O(-2, -1) across the line y = -5:
- The line y = -5 is a horizontal line that is 5 units below the x-axis.
- To reflect a point across a horizontal line, you need to keep the x-coordinate the same and change the sign of the y-coordinate.
- So the image of point O(-2, -1) after reflecting across the line y = -5 is O'(-2, 5-1) = O'(-2, 6).
2. Reflect the point O'(-2, 6) across the line x = 1:
- The line x = 1 is a vertical line passing through the point (1, 0).
- To reflect a point across a vertical line, you need to keep the y-coordinate the same and change the sign of the x-coordinate.
- So the image of point O'(-2, 6) after reflecting across the line x = 1 is O''(-1-1, 6) = O''(-2, 6).
(Note: We subtract 1 from the x-coordinate because the line x = 1 is 1 unit to the right of the y-axis.)
Therefore, the final image of point O after the two reflections is O''(-2, 6) which corresponds to the answer choice (-2, 6).