what line of reflection would change both the x and y coordinates of a point? choose all

Question

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