Question

identifying the rule for a composition of transformations
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

First, observe the horizontal and vertical shifts. The rectangle PQRS moves up by 2 units. The translation $T_{0,2}(x,y)=(x,y + 2)$ represents a vertical translation of 2 units up.

Step2: Analyze rotation

Then, note the orientation change. The rectangle is rotated 270 - degrees counter - clockwise about the origin. The rotation $R_{0,270^{\circ}}(x,y)=(y,-x)$. When we first translate and then rotate, the composition $R_{0,270^{\circ}}\circ T_{0,2}(x,y)$ means we first apply the translation $T_{0,2}(x,y)=(x,y + 2)$ and then apply the rotation $R_{0,270^{\circ}}$ to the result.

Answer:

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