Question

reflect $(5,-4)$ across the $y$-axis. then reflect the result across the $x$-axis. what are the coordinates of the final point?

Explanation:

Step1: Reflect 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 \((5,-4)\), after reflection across the \(y\) - axis, we get \((- 5,-4)\).

Step2: Reflect the result 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 \((-5,-4)\), after reflection across the \(x\) - axis, we get \((-5,4)\).

Answer:

\((-5,4)\)