Question

find the image of (1,2) after a reflection about x = 3 followed by a reflection about x = 7. ( ? , ) enter the number that belongs in the green box.

Explanation:

Step1: Reflect over \( x = 3 \)

The formula for reflecting a point \( (x, y) \) over the vertical line \( x = a \) is \( (2a - x, y) \). For \( x = 3 \) and \( (1, 2) \), we calculate \( 2(3) - 1 = 6 - 1 = 5 \). So the image after first reflection is \( (5, 2) \).

Step2: Reflect over \( x = 7 \)

Using the same reflection formula for \( x = 7 \) and the point \( (5, 2) \), we get \( 2(7) - 5 = 14 - 5 = 9 \). The \( y \)-coordinate remains 2.

Answer:

9