Question

Point A (-3,2) is to be reflected over the vertical line x = 1. What are the coordinates of the image of A'?

A(-3,2) - A' ( _, 2)

Answer 1

To reflect a point across a vertical line, you need to find the distance from the point to the line and then move that distance to the opposite side of the line.

1. **Identify the original point and the line**: The original point is A(-3, 2), and the vertical line is given by x = 1.

2. **Calculate the distance from point A to the line**: The x-coordinate of point A is -3. The vertical line x = 1 is 1 - (-3) = 4 units to the right of point A.

3. **Determine the x-coordinate of the reflected point**: Since the line is to the right of point A, we will move 4 units to the right of the line to find the x-coordinate of the reflected point (A'). The x-coordinate would be:
\[
1 + 4 = 5
\]

4. **The y-coordinate remains the same**: Since we are reflecting over a vertical line, the y-coordinate does not change. Therefore, the y-coordinate remains 2.

5. **Final coordinates of the image A'**: Combining both coordinates, the coordinates of the image A' are:
\[
A' (5, 2)
\]

So, the coordinates of the image A' are \( (5, 2) \).