Question

which rule describes the composition of transformations that maps △jkl to △jkl?
r_{0,90^{circ}}circ t_{0, - 2}(x,y)
t_{0, - 2}circ r_{0,90^{circ}}(x,y)
r_{0,90^{circ}}circ t_{-2,0}(x,y)
t_{-2,0}circ r_{0,90^{circ}}(x,y)

Explanation:

Step1: Analyze rotation

First, observe that $\triangle{JKL}$ is rotated $90^{\circ}$ counter - clockwise about the origin. The rule for a $90^{\circ}$ counter - clockwise rotation about the origin $R_{0,90^{\circ}}$ is $(x,y)\to(-y,x)$.

Step2: Analyze translation

After rotation, the figure is translated 2 units down. The rule for a translation 2 units down $T_{0, - 2}$ is $(x,y)\to(x,y - 2)$.

Step3: Determine composition order

The rotation must happen first and then the translation. The notation $T_{0, - 2}\circ R_{0,90^{\circ}}(x,y)$ means apply the rotation $R_{0,90^{\circ}}$ first and then the translation $T_{0, - 2}$.

Answer:

The rule that describes the composition of transformations that maps $\triangle{JKL}$ to $\triangle{J''K''L''}$ is $T_{0, - 2}\circ R_{0,90^{\circ}}(x,y)$. So the answer is B. $T_{0, - 2}\circ R_{0,90^{\circ}}(x,y)$