Question
find the image of O(-2,-1) after two reflections, first across the line y=-4 and then across the line x=1
a(-2,-9)
b(4,-9)
c(-2,-7)
d(4,-7)
a(-2,-9)
b(4,-9)
c(-2,-7)
d(4,-7)
Answers
GPT 3.5
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 break it down into two steps.
1. Reflection across the line y = -4:
The point O(-2,-1) will be reflected across the line y = -4. Since the line of reflection is horizontal, only the y-coordinate of the point will change. The y-coordinate will be reflected across the line y = -4 and the x-coordinate will remain the same.
The distance between the y-coordinate of (-1) and the line y = -4 is 3 units, so when reflected, the y-coordinate will become -7.
The point O(-2,-1) after reflecting across the line y = -4 becomes O'(-2,-7).
2. Reflection across the line x = 1:
Next, we will reflect the point O'(-2,-7) across the line x = 1. Since the line of reflection is vertical, only the x-coordinate of the point will change. The x-coordinate will be reflected across the line x = 1 and the y-coordinate will remain the same.
The distance between the x-coordinate of (-2) and the line x = 1 is 3 units, so when reflected, the x-coordinate will become 4.
Therefore, the final image of point O(-2,-1) after two reflections is at (4, -7), which corresponds to option d(4,-7).
1. Reflection across the line y = -4:
The point O(-2,-1) will be reflected across the line y = -4. Since the line of reflection is horizontal, only the y-coordinate of the point will change. The y-coordinate will be reflected across the line y = -4 and the x-coordinate will remain the same.
The distance between the y-coordinate of (-1) and the line y = -4 is 3 units, so when reflected, the y-coordinate will become -7.
The point O(-2,-1) after reflecting across the line y = -4 becomes O'(-2,-7).
2. Reflection across the line x = 1:
Next, we will reflect the point O'(-2,-7) across the line x = 1. Since the line of reflection is vertical, only the x-coordinate of the point will change. The x-coordinate will be reflected across the line x = 1 and the y-coordinate will remain the same.
The distance between the x-coordinate of (-2) and the line x = 1 is 3 units, so when reflected, the x-coordinate will become 4.
Therefore, the final image of point O(-2,-1) after two reflections is at (4, -7), which corresponds to option d(4,-7).