Question

find the image of a(-3,5) after translating (x,y)(x - 6,y - 1) then reflecting across the line x = - 1
hint: try to graph
(4,-5)
(7,4)
(4,7)
(-5,4)

Explanation:

Step1: Translate the point

Given the translation rule \((x,y)\to(x - 6,y-1)\).
For the point \(A(-3,5)\), substitute \(x=-3\) and \(y = 5\) into the rule:
\(x'=-3-6=-9\), \(y'=5 - 1=4\).
So the translated point is \((-9,4)\).

Step2: Reflect the translated point across the line \(x=-1\)

The formula for reflecting a point \((x,y)\) across the line \(x = a\) is \((2a - x,y)\).
Here \(a=-1\) and the point is \((-9,4)\).
Substitute \(x=-9\) into \(2a - x\): \(2\times(-1)-(-9)=-2 + 9=7\).
The \(y\) - coordinate remains the same. So the reflected point is \((7,4)\).

Answer:

\((7,4)\) (corresponds to the second option)