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)
graph shows triangle with vertices e(1, -2), f(3, 4), d(5, -3) on a coordinate grid

Explanation:

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) across the \(x\) - axis is that the \(x\) - coordinate remains the same, and the \(y\) - coordinate changes its sign. So, if we have a point \((x,y)\), after reflection over the \(x\) - axis, it becomes \((x, - y)\).

Step2: Identify the coordinates of point D

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

Step3: Apply the reflection rule

Using the rule for reflection over the \(x\) - axis, for the point \(D(5,-3)\), the \(x\) - coordinate \(x = 5\) remains the same, and the \(y\) - coordinate \(y=-3\) changes its sign. So 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 \((5, 3)\))