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: Understand the transformation rules

The transformation \(r_{y - axis}\circ T_{1,2}(x,y)\) means first perform the translation \(T_{1,2}(x,y)=(x + 1,y+2)\) and then perform the reflection about the \(y -\)axis \(r_{y - axis}(x,y)=(-x,y)\). Let the coordinates of \(F\) be \((x,y)\). After translation \(T_{1,2}\), the coordinates become \((x + 1,y + 2)\). After reflection about the \(y -\)axis, the coordinates become \((-(x + 1),y + 2)\).
From the graph, assume the coordinates of \(F''\) is \((1,4)\). So we have the equation \(-(x + 1)=1\) and \(y + 2=4\).

Step2: Solve the equations

For \(-(x + 1)=1\), we get \(x+1=-1\), then \(x=-2\).
For \(y + 2=4\), we get \(y=2\).

Answer:

\((-2,2)\)