Question

reflect $(3,7)$ across the $x$-axis. then reflect the result across the $y$-axis. what are the coordinates of the final point?

Explanation:

Step1: Reflect across the x - axis

When reflecting a point \((x,y)\) across the \(x\) - axis, the rule is \((x,y)\to(x, - y)\).
For the point \((3,7)\), after reflection across the \(x\) - axis, we get \((3,-7)\).

Step2: Reflect the new point across the y - axis

When reflecting a point \((x,y)\) across the \(y\) - axis, the rule is \((x,y)\to(-x,y)\).
For the point \((3, - 7)\), after reflection across the \(y\) - axis, we get \((-3,-7)\).

Answer:

\((-3,-7)\)