Question

parallelogram fghj is the final image after the rule r_y - axis o t_1,2(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: Identify the transformation rule

The rule $r_{y - axis}\circ T_{1,2}(x,y)$ means first translate the point $(x,y)$ using the translation $T_{1,2}$ (which is $(x + 1,y+2)$) and then reflect the resulting - point over the y - axis (the rule for reflecting over the y - axis is $(-x,y)$).

Step2: Assume the original coordinates of point F

Let's assume the original coordinates of point F from the graph are $(x_0,y_0)$. By observing the graph, if we assume the grid - lines represent 1 unit each, the original coordinates of point F are $(1,0)$.

Step3: Apply the translation

Apply the translation $T_{1,2}$ to the point $(1,0)$. Using the rule $(x,y)\to(x + 1,y + 2)$, we get $(1+1,0 + 2)=(2,2)$.

Step4: Apply the reflection over the y - axis

Apply the reflection over the y - axis to the point $(2,2)$. Using the rule $(-x,y)$, we get $(-2,2)$.

Answer:

$(-2,2)$