Question

what are the coordinates of the image of vertex d after a reflection across the x - axis?
(5,2)
(-5,-3)
(-2,5)
(2,-5)

Explanation:

Step1: Recall reflection rule

When reflecting a point $(x,y)$ across the $x - axis$, the rule is $(x,y)\to(x, - y)$.

Step2: Identify original coordinates of D

The original coordinates of vertex D are $(5,-3)$.

Step3: Apply reflection rule

Using the rule $(x,y)\to(x, - y)$ with $x = 5$ and $y=-3$, we get $(5,-(-3))=(5,3)$.

Answer:

$(5,3)$

It seems there is a mistake in the provided options as the correct answer $(5,3)$ is not among them. If we assume there was a mis - typing in the problem setup and we work with the general process, for a point $(x,y)$ reflected across the $x$-axis, we change the sign of the $y$-coordinate. Given point D with coordinates $(5, - 3)$, after reflection across the $x$-axis, the new coordinates are $(5,3)$.