Question

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

Explanation:

Step1: Analyze translation

First, observe the horizontal and vertical shifts. The figure seems to move 2 units down. The translation rule for moving 2 units down is $T_{0,- 2}(x,y)=(x,y - 2)$.

Step2: Analyze rotation

Then, notice the rotation. The figure is rotated 90 - degrees counter - clockwise about the origin. The rotation rule for a 90 - degree counter - clockwise rotation about the origin is $R_{0,90^{\circ}}(x,y)=(-y,x)$.

Step3: Determine composition order

We need to first perform the translation and then the rotation. The composition of transformations is written with the transformation on the right being performed first. So the composition is $R_{0,90^{\circ}}\circ T_{0,-2}(x,y)$.

Answer:

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