Question

1. graph the image of ( a(-7,6) ) after a reflection in ( y=x ) followed by a reflection in ( x = 3 ).

Explanation:

Step1: Reflect across \(y = x\)

When reflecting a point \((x,y)\) across the line \(y=x\), the transformation rule is \((x,y)\to(y,x)\).
For the point \(A(-7,6)\), after reflection across \(y = x\), we get \(A_1=(6,-7)\).

Step2: Reflect across \(x = 3\)

The formula for reflecting a point \((x,y)\) across the vertical line \(x = a\) is \((x,y)\to(2a - x,y)\).
Here \(a = 3\) and the point is \(A_1=(6,-7)\). Then \(x=6\), \(y = - 7\).
Using the formula \(x'=2\times3-6\), \(y'=-7\).
\(x'=0\), \(y'=-7\)

Answer:

The image of \(A(-7,6)\) after the two - step reflection is \((0,-7)\)