Question

question
what is the image point of $(-5,-7)$ after the transformation $r_{180^{circ}}circ t_{0,0}$?
answer attempt 1 out of 2

Explanation:

Step1: Analyze the translation \(T_{0,0}\)

The translation \(T_{0,0}\) means moving the point \(0\) units in the \(x -\)direction and \(0\) units in the \(y -\)direction. So, if we have a point \((x,y)\), after \(T_{0,0}\), the point remains \((x,y)\). For the point \((- 5,-7)\), after \(T_{0,0}\), it is still \((-5,-7)\).

Step2: Analyze the rotation \(R_{180^{\circ}}\)

The rule for a \(180^{\circ}\) rotation about the origin \((x,y)\to(-x,-y)\).
When \(x=-5\) and \(y = - 7\), then \(-x=-(-5) = 5\) and \(-y=-(-7)=7\)

Answer:

\((5,7)\)