Question

1. quadrilateral efgh is transformed to create quadrilateral efgh. describe a sequence of transformations that could map efgh to efgh.

Explanation:

Step1: Reflect over the y - axis

Reflecting a point \((x,y)\) over the \(y\) - axis gives the point \((-x,y)\). This will flip the quadrilateral \(EFGH\) from the left - hand side of the \(y\) - axis to the right - hand side.

Step2: Translate down

After reflection, we need to move the reflected quadrilateral down. If we assume the \(y\) - coordinate of each point of the reflected quadrilateral, we can find the vertical distance between the reflected points (after step 1) and the target points \(E'F'G'H'\). Let's say the vertical distance is \(k\) units. For a point \((x,y)\) after reflection, translating it down \(k\) units gives the point \((x,y - k)\).

Answer:

Reflect quadrilateral \(EFGH\) over the \(y\) - axis and then translate the resulting quadrilateral down by 4 units.