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:

Step 1: Understand the transformation rule

The rule is ( r_{y\text{-axis}} \circ T_{1,2}(x, y) ), which means first translate by ( T_{1,2} ) (add 1 to ( x ), 2 to ( y )), then reflect over the y-axis (negate ( x )-coordinate).

Step 2: Let original coordinates of ( F ) be ( (x, y) )

After translation: ( (x + 1, y + 2) )
After reflection over y-axis: ( (- (x + 1), y + 2) )

Step 3: Identify coordinates of ( F'' ) from the graph

Assume ( F'' ) is at ( (2, 4) ) (based on typical grid interpretation, adjust based on actual graph; here, assume this for example).

Step 4: Set up equations for inverse transformation

Reverse the reflection first: ( x' = -2 ) (since reflection negates ( x )), then reverse translation: ( x = x' - 1 = -2 - 1 = -3 ), ( y = y'' - 2 = 4 - 2 = 2 ).

Answer:

(-3, 2)

（注：实际答案需根据图中( F'' )的准确坐标计算，此处假设坐标为(2,4)进行演示。若图中( F'' )实际坐标不同，需相应调整步骤3和4的数值。）