Question

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

Explanation:

Step1: Determine the axis of reflection

• Observe the positions of the figures. If we reflect over the \(y -\)axis, the \(x -\)coordinates of the points of \(ABCD\) will change their signs.

Step2: Calculate the translation in the \(x -\)direction

• Let's take a point, say \(A(-5,2)\). After reflection over the \(y -\)axis, its image is \((5,2)\). The corresponding point \(E(3,-1)\). The change in \(x\) is \(3 - 5=- 2\).

Step3: Calculate the translation in the \(y -\)direction

• After reflection, for the \(y -\)coordinate of the reflected point of \(A\) (which is \(2\)) and the \(y -\)coordinate of \(E(-1)\), the change in \(y\) is \(-1 - 2=-3\)

Answer:

Reflect over the \(y\)-axis, then translate \((x + (-2),y+(-3))\)