Question

identifying the rule for a composition of transformations
which rule describes the composition of transformations that maps rectangle pqrs to pqrs?
○ r₀,₂₇₀° ∘ t₀,₂(x,y)
○ r₀,₁₈₀° ∘ t₂,₀(x,y)
○ t₀,₂ ∘ r₀,₂₇₀°(x,y)
○ r₀,₂ ∘ t₀,₁₈₀°(x,y)

Explanation:

Step1: Analyze the translation

The rectangle PQRS is first translated. Notice that the shape moves 2 units up. The translation rule for moving a point $(x,y)$ 2 units up is $T_{0,2}(x,y)=(x,y + 2)$.

Step2: Analyze the rotation

After the translation, the rectangle is rotated 270 - degrees counter - clockwise about the origin. The rotation rule for a 270 - degree counter - clockwise rotation about the origin $R_{0,270^{\circ}}(x,y)=(y,-x)$. When we first translate and then rotate, the composition of transformations is written with the translation first and then the rotation, i.e., $R_{0,270^{\circ}}\circ T_{0,2}(x,y)$.

Answer:

$R_{0,270^{\circ}}\circ T_{0,2}(x,y)$