Question

reflect (5,5) over the x - axis. then translate the result down 3 units. what are the coordinates of the final point?

Explanation:

Step1: Reflect 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 \((5,5)\), after reflection over the \(x\) - axis, we get \((5,-5)\).

Step2: Translate down 3 units

When translating a point \((x,y)\) down \(k\) units, the rule is \((x,y)\to(x,y - k)\). Here \(k = 3\), and the point after reflection is \((5,-5)\). So, \((5,-5)\to(5,-5-3)\)

Answer:

\((5,-8)\)