Question

what is the image of $(7,-2)$ after a reflection over the line $y=-x$?

Explanation:

Step1: Recall the reflection formula

The formula for reflecting a point \((x,y)\) over the line \(y = -x\) is \((-y,-x)\).

Step2: Substitute the values

Given the point \((7,-2)\), substitute \(x = 7\) and \(y=-2\) into the formula.
For the \(x\)-coordinate of the image: \(-y=-(-2) = 2\).
For the \(y\)-coordinate of the image: \(-x=-7\).

Answer:

\((2,-7)\)