Question
Explain how you would find the coordinates of the image of (5, 2) if it was reflected over the x-axis and then that image was reflected over the y-axis. What would be the end result?
Answers
GPT-4o mini
To find the coordinates of the image of the point (5, 2) after it is reflected over the x-axis and then over the y-axis, we can follow these steps:
1. **Reflection over the x-axis**:
- When a point \((x, y)\) is reflected over the x-axis, the y-coordinate changes sign while the x-coordinate remains the same.
- Therefore, reflecting the point (5, 2) over the x-axis results in the point \((5, -2)\).
2. **Reflection over the y-axis**:
- Next, when a point \((x, y)\) is reflected over the y-axis, the x-coordinate changes sign while the y-coordinate remains the same.
- Reflecting the point (5, -2) over the y-axis results in the point \((-5, -2)\).
Thus, the end result after reflecting the point (5, 2) over the x-axis and then the y-axis is the coordinates \((-5, -2)\).
1. **Reflection over the x-axis**:
- When a point \((x, y)\) is reflected over the x-axis, the y-coordinate changes sign while the x-coordinate remains the same.
- Therefore, reflecting the point (5, 2) over the x-axis results in the point \((5, -2)\).
2. **Reflection over the y-axis**:
- Next, when a point \((x, y)\) is reflected over the y-axis, the x-coordinate changes sign while the y-coordinate remains the same.
- Reflecting the point (5, -2) over the y-axis results in the point \((-5, -2)\).
Thus, the end result after reflecting the point (5, 2) over the x-axis and then the y-axis is the coordinates \((-5, -2)\).