Question

Given:• A(3,-2)What are the coordinates of A' after a reflection about the line y = 1?0 (-1, -2)(3, 4)0 (-1,2)0 (-1,4)

Answer 1

The line y=1 is a horizontal line paralel to the x axis. This means that a reflection about it can't change the value of the x coordinate:

$A_x=3=A^{\prime}_x$

Regarding the y coordinate, in A we have that:

$\begin{gathered} A_y=-2 \\ y-A_y=1-(-2)=3 \end{gathered}$

Since A' is the reflection of A about line y=1 then we have that:

$\begin{gathered} y-A^{\prime}_y=-(y-A^{}_y))=-3 \\ y-A^{\prime}_y=1-A^{\prime}_y=-3 \\ A^{\prime}_y=1+3=4 \end{gathered}$

Then the coordinates of point A' are (3,4) and the correct answer is the second one.