Question

reflect (1, 4) over the x - axis. then translate the result up 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 \((1,4)\), after reflection over the \(x\) - axis, it becomes \((1,-4)\).

Step2: Translate up 3 units

When translating a point \((x,y)\) up \(k\) units, the rule is \((x,y)\to(x,y + k)\).
Here \(k = 3\), and the point after reflection is \((1,-4)\). So, \((1,-4)\to(1,-4 + 3)\).

Answer:

\((1,-1)\)