Question

what is the image point of $(8,-4)$ after the transformation $r_{x - axis}circ t_{-1,3}$?

Explanation:

Step1: Apply the translation \(T_{-1,3}\)

For a point \((x,y)\), the translation \(T_{a,b}\) gives \((x + a,y + b)\). Here \(a=-1\), \(b = 3\) and \((x,y)=(8,-4)\).
So, \((8+(-1),-4 + 3)=(7,-1)\)

Step2: Apply the reflection \(r_{x - axis}\)

The rule for reflection over the \(x\)-axis is \((x,y)\to(x,-y)\).
For the point \((7,-1)\), after reflection over the \(x\)-axis, we get \((7,1)\)

Answer:

\((7,1)\)