Question

translate (1, - 3) down 1 unit. then reflect the result over the x - axis. what are the coordinates of the final point?

Explanation:

Step1: Translate the point down 1 unit

When translating a point \((x,y)\) down \(a\) units, the new \(y\) - coordinate is \(y - a\). Here \(x = 1,y=-3,a = 1\).
The new \(y\) - coordinate is \(y-1=-3 - 1=-4\), and the \(x\) - coordinate remains the same. So the point after translation is \((1,-4)\).

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 \((1,-4)\), after reflection over the \(x\) - axis, the \(x\) - coordinate remains \(x = 1\), and the new \(y\) - coordinate is \(-(-4)=4\).

Answer:

\((1,4)\)