Question

which rule describes the composition of transformations that maps △jkl to △jkl?
○ r₀,₉₀° ∘ t₀,₋₂(x, y)
○ t₀,₋₂ ∘ r₀,₉₀°(x, y)
○ r₀,₉₀° ∘ t₋₂,₀(x, y)
○ t₋₂,₀ ∘ r₀,₉₀°(x, y)

Explanation:

Step1: Analyze translation

First, observe the change in position of the triangle. Notice that the triangle is translated 2 units down. The translation rule for moving a point $(x,y)$ 2 units down is $T_{0,- 2}(x,y)=(x,y - 2)$.

Step2: Analyze rotation

Then, observe that after the translation, the triangle is rotated 90 - degrees counter - clockwise about the origin. The rotation rule for rotating a point $(x,y)$ 90 - degrees counter - clockwise about the origin is $R_{0,90^{\circ}}(x,y)=(-y,x)$.

Step3: Determine the order of composition

The rotation is done after the translation. In function composition, we read from right to left. So the composition of transformations is $R_{0,90^{\circ}}\circ T_{0,-2}(x,y)$.

Answer:

$R_{0,90^{\circ}}\circ T_{0,-2}(x,y)$