Question

rhombus efgh is the image of rhombus efgh under a rotation 90° clockwise about the origin followed by a translation.
write the rules for the rotation and translation.
rotation: (x, y) ↦ (□, □)
translation: (x, y) ↦ (□, □)

Explanation:

Step1: Recall rotation rule

The rule for a \(90^{\circ}\) clockwise rotation about the origin is \((x,y)\to(y, -x)\).

Step2: Find translation rule

Let's take a point. For example, if we consider point \(E(-9,-5)\). After rotation \(90^{\circ}\) clockwise about the origin, it becomes \((-5,9)\). The image of \(E\) is \(E'(-1,0)\).
To get from \((-5,9)\) to \((-1,0)\), we add \(4\) to the \(x\) - coordinate (\(-5 + 4=-1\)) and subtract \(9\) from the \(y\) - coordinate (\(9-9 = 0\)). So the translation rule is \((x,y)\to(x + 4,y-9)\).

Answer:

Rotation: \((x,y)\to(y,-x)\)
Translation: \((x,y)\to(x + 4,y-9)\)