Question

translate (-1, 5) up 2 units. then reflect the result over the x - axis. what are the coordinates of the final point?

Explanation:

Step1: Translate the point up 2 units

When translating a point \((x,y)\) up \(k\) units, the new \(y\)-coordinate is \(y + k\). Here \(x=-1,y = 5,k = 2\).
The new \(y\)-coordinate is \(5+2=7\), and the \(x\)-coordinate remains \(-1\). So the translated point is \((-1,7)\).

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

When reflecting a point \((x,y)\) over the \(x\)-axis, the rule is \((x,y)\to(x,-y)\).
For the point \((-1,7)\), after reflection over the \(x\)-axis, the \(x\)-coordinate \(-1\) stays the same, and the \(y\)-coordinate becomes \(-7\).

Answer:

\((-1,-7)\)