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 point A(-3, 2) over the vertical line \( x = 1 \), we first need to determine the horizontal distance between point A and the line \( x = 1 \).
1. The x-coordinate of point A is -3.
2. The distance from point A to the line \( x = 1 \) is:
\[
d = 1 - (-3) = 1 + 3 = 4
\]
3. Since we are reflecting over the line, we will move 4 units to the right of the line \( x = 1 \).
4. The x-coordinate of the reflected point \( A' \) will then be:
\[
x' = 1 + 4 = 5
\]
5. The y-coordinate remains the same during reflection, so the y-coordinate of \( A' \) is 2.
Thus, the coordinates of the image \( A' \) after reflection are:
\[
A' (5, 2)
\]
1. The x-coordinate of point A is -3.
2. The distance from point A to the line \( x = 1 \) is:
\[
d = 1 - (-3) = 1 + 3 = 4
\]
3. Since we are reflecting over the line, we will move 4 units to the right of the line \( x = 1 \).
4. The x-coordinate of the reflected point \( A' \) will then be:
\[
x' = 1 + 4 = 5
\]
5. The y-coordinate remains the same during reflection, so the y-coordinate of \( A' \) is 2.
Thus, the coordinates of the image \( A' \) after reflection are:
\[
A' (5, 2)
\]