Triangle ABC has coordinates A(1, 4): B(3, -2): and C(4, 2). Find the coordinates of the image A’B’C’ after a reflection iver the x-axis.
Would it be
A’(-1, 4) B’(-2, -3) C’(-4, 2) ??
Not quite. You want (x,y) -> (x,-y)
A’(1, -4) B’(3, 2) C’(4, -2)
you did (mostly) a reflection over the y-axis.
Thank u!
Yes, you are correct. The coordinates of the image A’B’C’ after a reflection over the x-axis would be A’(-1, 4), B’(-2, -2), C’(4, -2).
To find the image of a point after reflecting over the x-axis, you simply need to keep the x-coordinate the same and change the sign of the y-coordinate. Let me explain how you can calculate it for each point.
1. For point A(1, 4):
- The x-coordinate remains the same: 1.
- The y-coordinate changes its sign: -4.
- Therefore, the image of point A' is (-1, -4).
2. For point B(3, -2):
- The x-coordinate remains the same: 3.
- The y-coordinate changes its sign: 2.
- Therefore, the image of point B' is (3, 2).
3. For point C(4, 2):
- The x-coordinate remains the same: 4.
- The y-coordinate changes its sign: -2.
- Therefore, the image of point C' is (4, -2).
So the coordinates of the image A’B’C’ after the reflection over the x-axis are A’(-1, -4), B’(3, 2), and C’(4, -2).