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′

Answer 1

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 $x=1$: $$x_{A^{\prime }}=x_{\text{line}}+\text{Distance}=1+4=5.$$ The y-coordinate remains the same, so $y_A=2$.

4. Final coordinates of the reflected point: Therefore, the coordinates of the image $A^{\prime }$ are (5, 2).

Thus, the coordinates of the image of A′ after reflection are $A^{\prime }=(5,2)$.