Question

question
what is the image point of $(-4,-5)$ after the transformation $t_{4,2}circ r_{y=x}$?
answer attempt 1 out of 2
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Explanation:

Step1: Understand the transformation

First, \(r_{y = x}\) is a reflection over the line \(y=x\). The rule for reflecting a point \((x,y)\) over the line \(y = x\) is \((x,y)\to(y,x)\). So, for the point \((-4,-5)\), after reflection over \(y=x\), it becomes \((-5,-4)\).

Step2: Apply the translation \(T_{4,2}\)

The rule for translation \(T_{a,b}\) is \((x,y)\to(x + a,y + b)\). Here \(a = 4\) and \(b=2\). For the point \((-5,-4)\) after translation \(T_{4,2}\), we have \(x=-5+4=-1\) and \(y=-4 + 2=-2\).

Answer:

\((-1,-2)\)