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 points

Assume \(A(-5,2)\), \(B(-3,4)\), \(C(-2,4)\), \(D(-1,2)\), \(E(1,-1)\), \(H(2,-3)\), \(G(3,-3)\), \(F(4,-1)\).
After reflection over \(x -\)axis, the rule is \((x,y)\to(x, - y)\). So \(A(-5,2)\to A'(-5,-2)\), \(B(-3,4)\to B'(-3,-4)\), \(C(-2,4)\to C'(-2,-4)\), \(D(-1,2)\to D'(-1,-2)\).

Step2: Calculate translation

To get from \(A'(-5,-2)\) to \(E(1,-1)\):
For \(x -\)coordinate: \(1-(-5)=6\).
For \(y -\)coordinate: \(-1-(-2) = 1\).

Answer:

\((x + 6,y+1)\)