Question

question
what is the image point of $(-6, -4)$ after the transformation $r_{180^{circ}} \circ t_{-3,0}$?
answer attempt 1 out of 2
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Explanation:

Step1: Translation

First, perform the translation \(T_{-3,0}\). The rule for translation \(T_{a,b}\) is \((x,y)\to(x + a,y + b)\). For \(T_{-3,0}\) and the point \((-6,-4)\), we have:
\((x,y)=(-6,-4)\), \(x'=x-3=-6 - 3=-9\), \(y'=y+0=-4\). So the point after translation is \((-9,-4)\).

Step2: Rotation

Next, perform the rotation \(R_{180^{\circ}}\). The rule for a \(180^{\circ}\) rotation about the origin is \((x,y)\to(-x,-y)\). For the point \((-9,-4)\), we have \(x''=-(-9) = 9\), \(y''=-(-4)=4\).

Answer:

\((9,4)\)