parallelogram fghj is the final image after the rule $r_{y - axis}circ t_{1,2}(x,y)$ was applied to…

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)

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)

Answer

Explanation:

Step1: Analyze the transformation rules

The transformation $r_{y - axis}\circ T_{1,2}(x,y)$ means first a translation $T_{1,2}(x,y)=(x + 1,y+2)$ and then a reflection over the $y - axis$ which changes $(x,y)$ to $(-x,y)$. Let the original coordinates of $F$ be $(x,y)$. After translation, the coordinates become $(x + 1,y + 2)$. After reflection over the $y - axis$, the coordinates become $(-(x + 1),y + 2)$.

Step2: Identify the coordinates of $F''$

From the graph, the coordinates of $F''$ are $(3,4)$. So we have the equations: $-(x + 1)=3$ and $y + 2=4$.

Step3: Solve for $x$

Solve $-(x + 1)=3$. Multiply both sides by - 1 to get $x+1=-3$. Then subtract 1 from both sides: $x=-3 - 1=-4$.

Step4: Solve for $y$

Solve $y + 2=4$. Subtract 2 from both sides: $y=4 - 2=2$.

Answer:

$(-4,2)$