Answer:
The coordinates of the reflected triangle are [tex]X'(x,y) = (-3,-2)[/tex], [tex]Y' (x,y) = (-5,1)[/tex] and [tex]Z'(x,y) = (2,-3)[/tex].
Step-by-step explanation:
Let be a point [tex](a,b)\in\mathbb{R}^{2}[/tex], reflections across x- and y-axes are represented by the following operations:
x-Axis reflection:
[tex]d = d'[/tex]
[tex]b - 0 = 0 - b'[/tex]
[tex]b' = -b[/tex]
y-Axis reflection:
[tex]d = d'[/tex]
[tex]a - 0 = 0 - a'[/tex]
[tex]a' = -a[/tex]
If we know that [tex]X (x,y) = (3,2)[/tex], [tex]Y(x,y) = (5,-1)[/tex] and [tex]Z (x,y) = (-2, 3)[/tex], the coordinates after both reflections are, respectively:
[tex]X'(x,y) = (-3,-2)[/tex]
[tex]Y' (x,y) = (-5,1)[/tex]
[tex]Z'(x,y) = (2,-3)[/tex]
The coordinates of the reflected triangle are [tex]X'(x,y) = (-3,-2)[/tex], [tex]Y' (x,y) = (-5,1)[/tex] and [tex]Z'(x,y) = (2,-3)[/tex].
