Question

find the composition of transformations that map abcd to ehgf. reflect over the x - axis, then translate (x+?, y+).

Explanation:

Step1: Find coordinates of \(A\) and \(E\)

Let \(A(-5,8)\). After reflection over \(x\) - axis, \(A'\) has coordinates \((-5,-8)\). \(E(-2,-3)\).
The \(x\) - coordinate change: \(-2-(-5)=3\).
The \(y\) - coordinate change: \(-3 - (-8)=5\).

Step2: Generalize the translation

For a point \((x,y)\) after reflection over \(x\) - axis \((x,-y)\), then translation \((x + 3,y+5)\)

Answer:

\(x + 3,y + 5\)