Question

parallelogram fghj is the final image after the rule $r_{y - axis} circ t_{1,2}(x,y)$ was applied to parallelogram fghj. what are the coordinates of vertex f of parallelogram fghj? $(-2,2)$ $(-2,6)$ $(-3,4)$ $(-4,2)$

Explanation:

Step1: Identify $F''$ coordinates

From the graph, $F'' = (2, 4)$

Step2: Reverse the transformation order

The rule is $r_{y-axis} \circ T_{1,2}(x,y)$, so reverse first: undo reflection over y-axis.
Reflection over y-axis rule: $(x,y) \to (-x,y)$. Reverse: $(x',y') \to (-x',y')$
$\text{Pre-reflection point} = (-2, 4)$

Step3: Undo translation $T_{1,2}$

Translation $T_{1,2}(x,y)=(x+1,y+2)$. Reverse: $(x',y') \to (x'-1,y'-2)$
$F = (-2-1, 4-2) = (-3, 4)$

Answer:

(-3, 4)