Question

which rule describes the composition of transformations that maps △bcd to △bcd? 1. $r_{y = -x}circ t_{5,-6}(x,y)$ 2. $t_{6,-5}circ r_{y - axis}(x,y)$ 3. $r_{y - axis}circ t_{6,-5}(x,y)$ 4. $t_{5,-6}circ r_{y=-x}(x,y)$

Explanation:

Step1: Analyze translation

First, observe the horizontal and vertical shifts. The triangle moves 6 units to the left and 5 units down. The translation rule for a point \((x,y)\) is \(T_{- 6,-5}(x,y)=(x - 6,y - 5)\).

Step2: Analyze reflection

Then, note the reflection. The triangle is reflected over the \(y\) - axis. The reflection rule over the \(y\) - axis for a point \((x,y)\) is \(r_{y - axis}(x,y)=(-x,y)\). In a composition of transformations, we apply the translation first and then the reflection. So the composition is \(r_{y - axis}\circ T_{-6,-5}(x,y)\).

Answer:

\(r_{y - axis}\circ T_{-6,-5}(x,y)\)