Given:
The given coordinate is (1,2).
The obective is to find the image of (1,2) after a reflection about x=3 followed by x=7.
Consider the coordinate as (x1, y1) = (1,2).
The distance between the given coordinate and the line x= 3 can be calculated as,
[tex]\begin{gathered} d=x-x1 \\ d=3-1 \\ d=2 \end{gathered}[/tex]After the reflection, the coordinate will shift to d more the x = 3.
So the coordinate (x2, y2) can be calculated as,
[tex]\begin{gathered} x_2=d+x \\ x_2=2+3 \\ x_2=5 \end{gathered}[/tex]Thus, the coordinate will be (x2, y2) = (5, 2).
Now, the distance between the coordinate (x2, y2) and x-7 can be calculated as,
[tex]\begin{gathered} d=x-x_2 \\ d=7-5 \\ d=2 \end{gathered}[/tex]After the reflection, the coordinate will shift to d more than x = 7.
So the coordinate (x3, y3) can be calculated as,
[tex]\begin{gathered} x_3=x+d \\ =7+2 \\ =9 \end{gathered}[/tex]Hence, the image of (1,2) after reflection ove x = 3 and x= 7 will be (9,2).
