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 - degree clockwise rotation about the origin is $(x,y)\to(y, - x)$.

Step2: Analyze translation

Let's assume a point $(x,y)$ after rotation is $(y,-x)$. To find the translation, we can pick a corresponding point. For example, if we consider point $E(-8,-5)$ in the original rhombus. After 90 - degree clockwise rotation about the origin, it becomes $E'(-5,8)$. In the graph, the final position of the corresponding point of $E$ is $E'(-1,0)$. To get from $(-5,8)$ to $(-1,0)$, we add 4 to the $x$ - coordinate and subtract 8 from the $y$ - coordinate. So the translation rule is $(x,y)\to(x + 4,y-8)$.

Answer:

Rotation: $(x,y)\to(y,-x)$
Translation: $(x,y)\to(x + 4,y - 8)$