Question

question
what is the image point of (3, -6) after the transformation ( t_{4,3} circ r_{\text{y-axis}} )?
answer attempt 1 out of 2

Explanation:

Step1: Apply reflection over y - axis

The reflection over the \(y\) - axis, \(r_{y - \text{axis}}\), has the rule \((x,y)\to(-x,y)\). For the point \((3,-6)\), applying \(r_{y - \text{axis}}\), we get \((- 3,-6)\).

Step2: Apply translation \(T_{4,3}\)

The translation \(T_{4,3}\) has the rule \((x,y)\to(x + 4,y+3)\). We take the result from the previous step \((-3,-6)\) and apply the translation. So \(x=-3 + 4=1\) and \(y=-6 + 3=-3\).

Answer:

\((1,-3)\)