Question

find the coordinates of point d after point d is reflected across the x-axis. list the coordinates of point d. d (\boxed{ }, ? ) d (-1,3)

Explanation:

Step1: Recall reflection rule over x - axis

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 \((x,y)\) across the \(x\) - axis is \((x,y)\to(x, -y)\).

Step2: Apply the rule to point \(D(-1,3)\)

For point \(D(-1,3)\), the \(x\) - coordinate is \(-1\) and the \(y\) - coordinate is \(3\). Using the reflection rule across the \(x\) - axis, the \(x\) - coordinate of \(D'\) will be the same as that of \(D\), i.e., \(-1\), and the \(y\) - coordinate of \(D'\) will be \(-3\) (since we change the sign of the \(y\) - coordinate of \(D\)). So, the coordinates of \(D'\) are \((-1,-3)\).

Answer:

\(D'(-1, -3)\)