Question

what is the image point of $(-4,9)$ after the transformation $r_{90^{circ}}circ t_{0,5}$?

Explanation:

Step1: Translation

First, perform the translation \(T_{0,5}\). The rule for translation \(T_{a,b}\) is \((x,y)\to(x + a,y + b)\). For \(T_{0,5}\), when the point is \((-4,9)\), we have \(x=-4,y = 9,a = 0,b = 5\).

$$
LATEXBLOCK0
$$

The point after translation is \((-4,14)\).

Step2: Reflection

Next, perform the reflection \(R_{y - axis}\). The rule for reflection about the \(y\) - axis is \((x,y)\to(-x,y)\). For the point \((-4,14)\), we have \(x=-4,y = 14\).

$$
LATEXBLOCK1
$$

Answer:

\((4,14)\)