Question
vertical line of reflection. The coordinates of vertices A , B , C , and B′ are shown. What are the coordinates of vertex A′ ?
Answers
Answered by
GPT-4o mini
To determine the coordinates of the vertex \( A' \) after reflecting point \( A \) over a vertical line of reflection, you first need to know the coordinates of point \( A \) and the equation of the vertical line of reflection.
In general, if the vertical line of reflection is given by \( x = k \), where \( k \) is a constant, then the reflection of a point \( (x_A, y_A) \) across this line can be calculated as follows:
1. **Subtract \( k \) from \( x_A \)**: This gives you the distance from the line to point \( A \).
2. **Reflect this distance across the line**: The reflected distance from the line will be \( k - (x_A - k) = 2k - x_A \).
3. **Keep the \( y \)-coordinate the same**: The \( y_A \) coordinate remains unchanged.
So the coordinates of \( A' \) will be:
\[
A' = (2k - x_A, y_A)
\]
If you provide the specific coordinates of vertex \( A \) and the equation of the vertical line of reflection, I can help you find \( A' \) more accurately.
In general, if the vertical line of reflection is given by \( x = k \), where \( k \) is a constant, then the reflection of a point \( (x_A, y_A) \) across this line can be calculated as follows:
1. **Subtract \( k \) from \( x_A \)**: This gives you the distance from the line to point \( A \).
2. **Reflect this distance across the line**: The reflected distance from the line will be \( k - (x_A - k) = 2k - x_A \).
3. **Keep the \( y \)-coordinate the same**: The \( y_A \) coordinate remains unchanged.
So the coordinates of \( A' \) will be:
\[
A' = (2k - x_A, y_A)
\]
If you provide the specific coordinates of vertex \( A \) and the equation of the vertical line of reflection, I can help you find \( A' \) more accurately.