Question

which rule describes the composition of transformations that maps pre - image abcd to final image a\b\c\d\?
○ $r_{x - axis}circ t_{- 6,1}(x,y)$
○ $t_{- 6,1}circ r_{x - axis}(x,y)$
○ $r_{0,90^{circ}}circ t_{- 6,1}(x,y)$
○ $t_{- 6,1}circ r_{0,90^{circ}}(x,y)$

Explanation:

Step1: Analyze translation

First, observe that the pre - image ABCD is translated. The notation $T_{- 6,1}(x,y)=(x - 6,y + 1)$ means a translation 6 units to the left and 1 unit up.

Step2: Analyze reflection

Then, observe that after translation, the figure is reflected over the x - axis. The rule for reflection over the x - axis is $r_{x - axis}(x,y)=(x,-y)$. The order of composition matters. The correct order is first translation and then reflection, which is written as $T_{-6,1}\circ r_{x - axis}(x,y)$.

Answer:

$T_{-6,1}\circ r_{x - axis}(x,y)$