Question

find the composition of transformations that maps \\( \triangle abc \\) to \\( \triangle a ^ { prime } b ^ { prime } c ^ { prime } \\).
reflect over the \\( x - \\) axis, then translate \\( ( x + ? , y + ) \\).

Explanation:

Step1: Find coordinates

Coordinates of \(A(-4,2)\), \(B(-2,4)\), \(C(-2,2)\); coordinates of \(A'(0,-3)\), \(B'(0,-5)\), \(C'(2,-3)\)

Step2: Reflect over \(x -\)axis

After reflection over \(x -\)axis, \(A(-4,2)\to A_1(-4,-2)\), \(B(-2,4)\to B_1(-2,-4)\), \(C(-2,2)\to C_1(-2,-2)\)

Step3: Find translation rule

For \(x -\)coordinate: \(0-(-4)=4\); for \(y -\)coordinate: \(-3-(-2)=-1\)

Answer:

\((x + 4,y-1)\)