Question

what is the image point of (7, 3) after the transformation $r_{y\text{-axis}} \circ t_{-5,1}$?
answer attempt 1 out of 2
(\boxed{-2}, \boxed{4}) submit answer

Explanation:

Step1: Perform translation

The translation \(T_{-5,1}\) means we subtract \(5\) from the \(x -\)coordinate and add \(1\) to the \(y -\)coordinate.
For the point \((7,3)\), after translation:
\(x = 7-5=2\), \(y = 3 + 1=4\). The point becomes \((2,4)\).

Step2: Perform reflection over the \(y -\)axis

The rule for reflection over the \(y -\)axis is \((x,y)\to(-x,y)\).
For the point \((2,4)\), after reflection: \(x=-2\), \(y = 4\).

Answer:

\((-2,4)\)