Question

the point k(1, 4) is reflected over the x - axis. what are the coordinates of the resulting point, k?

Explanation:

Step1: Recall reflection over x - axis rule

When a point \((x,y)\) is reflected over the \(x\) - axis, the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign. The formula for the reflection of a point \((x,y)\) over the \(x\) - axis is \((x,y)\to(x, - y)\).

Step2: Apply the rule to point \(K(1,4)\)

For the point \(K(1,4)\), where \(x = 1\) and \(y=4\), after reflecting over the \(x\) - axis, the \(x\) - coordinate is still \(1\) and the \(y\) - coordinate becomes \(- 4\). So the coordinates of the resulting point \(K'\) are \((1,-4)\).

Answer:

\((1, - 4)\)