Question

what is the correct list of transformations to go from the pre - image triangle to the final image triangle?
o $r_{x - axis}$ and then $t_{(x + 6,y + 2)}$
o $t_{(x - 6,y - 2)}$ and then $r_{x - axis}$
o $r_{x - axis}$ and then $t_{(x + 7,y + 3)}$
o $r_{y - axis}$ and then $t_{(x + 6,y + 2)}$

Explanation:

Step1: Analyze reflection

First, observe that the pre - image triangle is reflected over the y - axis. When a point $(x,y)$ is reflected over the y - axis, the transformation is $(x,y)\to(-x,y)$.

Step2: Analyze translation

Then, count the horizontal and vertical displacements. The x - coordinate of each point of the reflected triangle is increased by 6 (right - shift) and the y - coordinate is increased by 2 (up - shift), which is the translation $T_{(x + 6,y+2)}$.

Answer:

$r_{y - axis}$ and then $T_{(x + 6,y+2)}$