Question

question 1-12
determine the coordinates of a after a reflection of pre - image a (7, - 6) across the line y = x followed by a reflection across the line x = - 3
graph a below

Explanation:

Step1: Reflect over \( y = x \)

To reflect a point \((x, y)\) over the line \( y = x \), we swap the \( x \)- and \( y \)-coordinates. For the pre - image \( A(7,-6) \), after reflection over \( y = x \), the new coordinates \( A' \) will be \((-6,7)\).

Step2: Reflect over \( x=-3 \)

The formula for reflecting a point \((x,y)\) over the vertical line \( x = a \) is \( x'=2a - x \), \( y' = y \). Here, \( a=-3 \) and the point we are reflecting is \( A'(-6,7) \).
First, calculate the new \( x \)-coordinate: \( x'=2\times(-3)-(-6)=-6 + 6=0 \). The \( y \)-coordinate remains the same, so \( y' = 7 \). So the coordinates of \( A'' \) are \((0,7)\).

Answer:

\((0,7)\)