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

By observing the positions of the corresponding points of the two figures (e.g., point \(A\) and point \(E\), point \(B\) and point \(H\)), we can see that the reflection is over the \(y\) - axis. When reflecting a point \((x,y)\) over the \(y\) - axis, the transformation rule is \((x,y)\to(-x,y)\).

Step2: Calculate the translation

Let's take a pair of corresponding points. For example, take point \(B(- 3,4)\) (after reflection over the \(y\) - axis, it becomes \((3,4)\)) and point \(H(-1,0)\).
For the \(x\) - coordinate: Let \(x_1 = 3\) (after reflection) and \(x_2=-1\). We use the formula \(x_2=x_1 + a\), so \(-1=3 + a\), then \(a=-4\).
For the \(y\) - coordinate: Let \(y_1 = 4\) (after reflection) and \(y_2 = 0\). We use the formula \(y_2=y_1 + b\), so \(0 = 4 + b\), then \(b=-4\).

Answer:

Reflect over the \(y\) - axis, then translate \((x - 4,y-4)\)