which rule describes the composition of transformations that maps △jkl to △jkl?\n$r_{0,90^{circ}}circ t_{0…

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

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

Answer

Explanation:

Step1: Analyze translation

First, observe the change in the position of the triangle in the x - y plane. Notice that the triangle is first translated. Looking at the x - coordinates of corresponding points, we can see that the x - coordinate of each point of $\triangle{JKL}$ is decreased by 2 to get to an intermediate position before rotation. The translation rule for moving 2 units to the left is $T_{- 2,0}(x,y)=(x - 2,y)$.

Step2: Analyze rotation

After the translation, the triangle is rotated 90 degrees counter - clockwise about the origin. The rotation rule for a 90 - degree counter - clockwise rotation about the origin is $R_{0,90^{\circ}}(x,y)=(-y,x)$. In a composition of transformations, the transformation that is applied first is on the right - hand side of the composition symbol $\circ$. So the composition of transformations that maps $\triangle{JKL}$ to $\triangle{J''K''L''}$ is $R_{0,90^{\circ}}\circ T_{-2,0}(x,y)$.

Answer:

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