Question

translate (-2, 2) up 1 unit. then reflect the result over the y - axis. what are the coordinates of the final point?

Explanation:

Step1: Translate the point up 1 unit

When translating a point \((x,y)\) up \(k\) units, the new \(y\) - coordinate is \(y + k\). For the point \((-2,2)\) translated up 1 unit (\(k = 1\)), the new point is \((-2,2 + 1)=(-2,3)\).

Step2: Reflect the translated point over the \(y\) - axis

When reflecting a point \((x,y)\) over the \(y\) - axis, the rule is \((x,y)\to(-x,y)\). For the point \((-2,3)\), after reflection over the \(y\) - axis, the new \(x\) - coordinate is \(-(-2)=2\) and the \(y\) - coordinate remains \(3\). So the new point is \((2,3)\).

Answer:

\((2,3)\)