Question

what are the coordinates of the image of vertex d after a reflection across the x-axis?
(5, 3)
(-5, -3)
(-3, 5)
(3, -5)

Explanation:

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) across the \(x\) - axis is \((x,-y)\) (the \(x\) - coordinate remains the same, and the \(y\) - coordinate changes its sign).

Step2: Identify coordinates of point D

From the graph, the coordinates of point \(D\) are \((5,-3)\).

Step3: Apply the reflection rule

Using the rule \((x,y)\to(x,-y)\) for the point \(D(5,-3)\), we substitute \(x = 5\) and \(y=-3\) into the rule. The new \(x\) - coordinate is still \(5\), and the new \(y\) - coordinate is \(-(-3)=3\). So the image of \(D\) after reflection across the \(x\) - axis is \((5,3)\).

Answer:

\((5, 3)\) (corresponding to the option with text \((5, 3)\))