Question

which rule describes the composition of transformations that maps rectangle pqrs to p\q
\s\?
$r_{0,270^{circ}}circ t_{0,2}(x,y)$
$r_{0,180^{circ}}circ t_{2,0}(x,y)$
$t_{0,2}circ r_{0,270^{circ}}(x,y)$
$r_{0,2}circ t_{0,180^{circ}}(x,y)$

Explanation:

Step1: Analyze translation

The rectangle PQRS is first translated 2 units up. The translation rule for moving a point $(x,y)$ 2 units up is $T_{0,2}(x,y)=(x,y + 2)$.

Step2: Analyze rotation

After the translation, the rectangle is rotated 270 - degrees counter - clockwise about the origin. The rule for rotating a point $(x,y)$ 270 - degrees counter - clockwise about the origin is $R_{0,270^{\circ}}(x,y)=(y,-x)$. The composition of transformations is first the translation and then the rotation, written as $R_{0,270^{\circ}}\circ T_{0,2}(x,y)$.

Answer:

$R_{0,270^{\circ}}\circ T_{0,2}(x,y)$