The question is: find the image of o(-2 -1) after two reflections, first across the line y=-5, then across the line x=1, I'm confused because I reflected it across the y access and got -7,-6 then I reflected it x=1 and Got -6,-5, But that is not in the answers. I know I did something wrong could you help me by telling me which step I did wrong Please, and Thank you
It helps to make a sketch in this case, I assume you did that
(-2,-1) ---reflect in y=-5 ---> (-2,-9)
notice the midpoint of these points lies on y = -5
(-2,-9) ---reflect in x = 1)---> (4,-9)
again, notice the midpoint of these two points
lies on the line x = 1
Ooh, Thank you so much I realized I was subtracting 5 from both points not just Y
To find the image of point O(-2, -1) after two reflections, first across the line y = -5, and then across the line x = 1, you need to follow these steps:
1. Reflect across the line y = -5:
- The line y = -5 is a horizontal line passing through the point (-2, -5).
- 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.
- Applying this, the image of O(-2, -1) after reflecting across y = -5 would be O'(-2, -9).
2. Reflect O'(-2, -9) across the line x = 1:
- The line x = 1 is a vertical line passing through the point (1, -9).
- 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.
- Applying this, the image of O'(-2, -9) after reflecting across x = 1 would be O''(3, -9).
Therefore, the correct answer should be O''(3, -9), not O'(-6, -5) as you obtained in your calculations.
Double-checking your steps, it seems that you incorrectly reflected O'(-2, -9) across the line x = 1. Make sure you correctly change the sign of the x-coordinate, not the y-coordinate, when reflecting across a vertical line.
Hope this clears up any confusion!