Question

parallelogram fghj is the final image after the rule r - y - axis o t1,2(x, y) was applied to parallelogram fghj. what are the coordinates of vertex f of parallelogram fghj? (-2, 6) (-4, 2) (-2, 2) (-3, 4)

Explanation:

Step1: Analyze the transformation rules

The transformation rule is a composition of a translation $T_{1,2}(x,y)=(x + 1,y+2)$ and a reflection over the y - axis. Let the original coordinates of point $F$ be $(x,y)$. After translation $T_{1,2}$, the coordinates become $(x + 1,y + 2)$. After reflection over the y - axis, the x - coordinate changes its sign. Let's work backward from the final - image point.

Step2: Assume the final - image coordinates of $F$

From the graph, assume the coordinates of $F''$ are $(3,4)$.

Step3: Reverse the y - axis reflection

To reverse the y - axis reflection, if a point $(a,b)$ is the result of reflecting a point $(x,b)$ over the y - axis, then $x=-a$. So if the point after reflection is $(3,4)$, the point before reflection (after translation) is $(-3,4)$.

Step4: Reverse the translation

The translation rule is $T_{1,2}(x,y)=(x + 1,y+2)$. To reverse it, we use the rule $T_{- 1,-2}(x,y)=(x - 1,y - 2)$. For the point $(-3,4)$, applying the reverse - translation: $x=-3-1=-4$ and $y=4 - 2=2$.

Answer:

$(-4,2)$