which rule describes a composition of transformations that maps pre - image pqrs to image pqrs?\n$r_{0,270^{c…

which rule describes a composition of transformations that maps pre - image pqrs to image pqrs?\n$r_{0,270^{circ}}circ t_{- 2,0}(x,y)$\n$t_{-2,0}circ r_{0,270^{circ}}(x,y)$\n$r_{0,270^{circ}}circ r_{y - axis}(x,y)$\n$r_{y - axis}circ r_{0,270^{circ}}(x,y)$

which rule describes a composition of transformations that maps pre - image pqrs to image pqrs?\n$r_{0,270^{circ}}circ t_{- 2,0}(x,y)$\n$t_{-2,0}circ r_{0,270^{circ}}(x,y)$\n$r_{0,270^{circ}}circ r_{y - axis}(x,y)$\n$r_{y - axis}circ r_{0,270^{circ}}(x,y)$

Answer

Answer:

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

Explanation:

Step1: Analyze translation

The pre - image is shifted 2 units left. Translation $T_{-2,0}(x,y)=(x - 2,y)$.

Step2: Analyze rotation

After translation, a $270^{\circ}$ counter - clockwise rotation about the origin $R_{0,270^{\circ}}(x,y)=(y,-x)$ is applied. Composition is done from right to left. First translation then rotation gives the correct transformation from $PQRS$ to $P''Q''R''S''$.