Question

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point p is reflected across the x-axis to form point q. what are the coordinates of point q? (\boxed{ }, ? ) \text{ image shows coordinate plane with } p(5,15) \text{, } x\text{-axis from } -25 \text{ to } 25, y\text{-axis from } -25 \text{ to } 25, and point } q \text{ below the } x\text{-axis}

Explanation:

Step1: Recall reflection over x - axis rule

When a point \((x,y)\) is reflected across 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 \(P(5,15)\)

For point \(P\) with coordinates \((5,15)\), the \(x\) - coordinate is \(5\) and the \(y\) - coordinate is \(15\). After reflecting across the \(x\) - axis, the \(x\) - coordinate of the image point \(Q\) will be the same as that of \(P\), i.e., \(x = 5\), and the \(y\) - coordinate will be \(- 15\) (since we change the sign of the \(y\) - coordinate of \(P\)).

Answer:

\((5, - 15)\)