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 translation

We can see that the triangle is first translated vertically down by 2 units. The rule for a vertical - translation of 2 units down is $T_{0,-2}(x,y)=(x,y - 2)$.

Step2: Analyze rotation

After the translation, the triangle is rotated 90 - degrees counter - clockwise about the origin. The rule for a 90 - degree counter - clockwise rotation about the origin is $R_{0,90^{\circ}}(x,y)=(-y,x)$. When we have a composition of transformations, the order matters. We first perform the translation and then the rotation. The composition of transformations is written as $R_{0,90^{\circ}}\circ T_{0,-2}(x,y)$.

Answer:

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