Question

what line of reflection would change both the x and y coordinates of a point? choose all
origin
y-axis
y=x
x axis
y=0
y=-x

Answer 1

To determine which lines of reflection would change both the x and y coordinates of a point, let's analyze each option:

1. **Origin**: Reflecting across the origin changes both coordinates: \((x, y) \rightarrow (-x, -y)\). **(Changes both)**

2. **y-axis**: Reflecting across the y-axis changes the x-coordinate but leaves the y-coordinate unchanged: \((x, y) \rightarrow (-x, y)\). **(Does not change both)**

3. **y = x**: Reflecting across the line \(y = x\) swaps the coordinates: \((x, y) \rightarrow (y, x)\). **(Changes both)**

4. **x-axis**: Reflecting across the x-axis changes the y-coordinate but leaves the x-coordinate unchanged: \((x, y) \rightarrow (x, -y)\). **(Does not change both)**

5. **y = 0**: This is the same as reflecting across the x-axis, so it changes the y-coordinate only: \((x, y) \rightarrow (x, -y)\). **(Does not change both)**

6. **y = -x**: Reflecting across the line \(y = -x\) changes both coordinates: \((x, y) \rightarrow (-y, -x)\). **(Changes both)**

In summary, the lines of reflection that change both the x and y coordinates of a point are:

- **Origin**
- **y = x**
- **y = -x**