Question

Segment JK has endpoints J(2, 4) and K(6, 2). You dilate the segment using a dilation centered at the origin with a scale factor of ½ and then reflect the image over the x-axis. What is the midpoint of the final image?

Answer 1

SOLUTION

$\begin{gathered} J(2,4) \\ k(6,2) \end{gathered}$

DILATION BY SCALE FACTORN OF 1/2

$\begin{gathered} J^{\prime}(1,2) \\ K^{\prime}(3,1) \end{gathered}$

REFLECTED OVER THE X-AXIS

$\begin{gathered} J^{\prime}(1,-2) \\ K^{\prime}(3,-1) \end{gathered}$

MIDPOINT OF THE FINAL IMAGE

$\begin{gathered} (\frac{1+3}{2},\frac{-2+(-1)}{2} \\ (2,\frac{-3}{2}) \end{gathered}$