Answer:
Step-by-step explanation:
Let [tex](a,b)\in \mathbb{R}^{2}[/tex], a reflection over the x-axis consists in the following operation:
[tex](a,b) \rightarrow (a,-b)[/tex]
If we know that [tex]X = (-4,3)[/tex] and [tex]Y = (2, 3)[/tex], then the points translated over the x-axis are [tex]X' = (-4, -3)[/tex] and [tex]Y' = (2,-3)[/tex], respectively. The most precise description of the shape is a rectangle for the following facts:
1) [tex]XX' = YY' = 8[/tex] and [tex]XY = X'Y' = 6[/tex].
2) [tex]X[/tex] and [tex]X'[/tex] have the same x-component.
3) [tex]Y[/tex] and [tex]Y'[/tex] have the same x-component.
4) [tex]X[/tex] and [tex]Y[/tex] have the same y-component.
5) [tex]X'[/tex] and [tex]Y'[/tex] have the same y-component.
A representation of the shape is included below as attachment.
