Question

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

Explanation:

Step1: Analyze translation

First, observe the movement from the original figure ABCD to an intermediate - figure (say A'B'C'D'). The figure seems to be translated. The translation rule $T_{-6,1}(x,y)=(x - 6,y + 1)$ means moving each point of the figure 6 units to the left and 1 unit up.

Step2: Analyze reflection

Then, observe the movement from the intermediate - figure A'B'C'D' to the final figure A''B''C''D''. The figure is reflected over the x - axis. The reflection rule over the x - axis is $r_{x - axis}(x,y)=(x,-y)$.

Step3: Determine composition order

The composition of transformations should first perform the translation and then the reflection. The notation for composition of transformations is read from right to left. So the composition of transformations that maps pre - image ABCD to final image A''B''C''D'' is $r_{x - axis}\circ T_{-6,1}(x,y)$.

Answer:

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