Question
Point A(−3,2) is to be reflected over the vertical line x=1 . What are the coordinates of the image of A′ ? (1 point) A(−3,2)→A′
Answers
GPT-4o mini
To reflect a point over a vertical line, you can follow these steps:
1. **Identify the line of reflection**: In this case, the line is \( x = 1 \).
2. **Determine the distance from the point to the line of reflection**: For point A(-3, 2), the distance to the line \( x = 1 \) is calculated as follows:
\[
\text{Distance} = |x_A - x_{\text{line}}| = |-3 - 1| = |-4| = 4.
\]
3. **Reflect the point**: To find the reflected point A′, you will move 4 units to the right of the line \( x = 1 \):
\[
x_{A'} = x_{\text{line}} + \text{Distance} = 1 + 4 = 5.
\]
The y-coordinate remains the same, so \( y_A = 2 \).
4. **Final coordinates of the reflected point**: Therefore, the coordinates of the image \( A' \) are (5, 2).
Thus, the coordinates of the image of A′ after reflection are \( A' = (5, 2) \).
1. **Identify the line of reflection**: In this case, the line is \( x = 1 \).
2. **Determine the distance from the point to the line of reflection**: For point A(-3, 2), the distance to the line \( x = 1 \) is calculated as follows:
\[
\text{Distance} = |x_A - x_{\text{line}}| = |-3 - 1| = |-4| = 4.
\]
3. **Reflect the point**: To find the reflected point A′, you will move 4 units to the right of the line \( x = 1 \):
\[
x_{A'} = x_{\text{line}} + \text{Distance} = 1 + 4 = 5.
\]
The y-coordinate remains the same, so \( y_A = 2 \).
4. **Final coordinates of the reflected point**: Therefore, the coordinates of the image \( A' \) are (5, 2).
Thus, the coordinates of the image of A′ after reflection are \( A' = (5, 2) \).