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what is the image of $(-1,7)$ after a reflection over the line $y = x$?
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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 \((-1,7)\), swap the \(x\) - coordinate and \(y\) - coordinate. So, \(x=-1\) and \(y = 7\) become \(x = 7\) and \(y=-1\).
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\((7,-1)\)