Question

what is the image of $(2,-4)$ after a reflection over the line $y = x$?

Explanation:

Step1: Recall the reflection rule

When reflecting a point \((x,y)\) over the line \(y = x\), the rule is \((x,y)\to(y,x)\).

Step2: Apply the rule to the given point

For the point \((2,-4)\), swap the \(x\) - coordinate and \(y\) - coordinate. So, \(x = 2\) and \(y=-4\) become \(x=-4\) and \(y = 2\).

Answer:

\((-4,2)\)