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

First, observe the vertical - shift. Rectangle PQRS moves 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

Then, observe the rotation. After the translation, the rectangle is rotated 270° counter - clockwise about the origin. The rotation rule for rotating a point (x,y) 270° counter - clockwise about the origin is \(R_{0,270^{\circ}}(x,y)=(y,-x)\). In a composition of transformations, the transformation that is applied first is on the right - hand side of the composition notation. So the composition of transformations that maps rectangle PQRS to P''Q''R''S'' is \(R_{0,270^{\circ}}\circ T_{0,2}(x,y)\).

Answer:

The correct rule is \(R_{0,270^{\circ}}\circ T_{0,2}(x,y)\) (the first option with the correct composition order).