Question

A triangle with the coordinates X(3, 2), Y(5, -1), and Z(-2, 3) is reflected across both the x- and y-axes. The coordinates after both reflections are what

Answer 1

Answer:

The coordinates of the reflected triangle are $X'(x,y) = (-3,-2)$, $Y' (x,y) = (-5,1)$ and $Z'(x,y) = (2,-3)$.

Step-by-step explanation:

Let be a point $(a,b)\in\mathbb{R}^{2}$, reflections across x- and y-axes are represented by the following operations:

x-Axis reflection:

$d = d'$

$b - 0 = 0 - b'$

$b' = -b$

y-Axis reflection:

$d = d'$

$a - 0 = 0 - a'$

$a' = -a$

If we know that $X (x,y) = (3,2)$, $Y(x,y) = (5,-1)$ and $Z (x,y) = (-2, 3)$, the coordinates after both reflections are, respectively:

$X'(x,y) = (-3,-2)$

$Y' (x,y) = (-5,1)$

$Z'(x,y) = (2,-3)$

The coordinates of the reflected triangle are $X'(x,y) = (-3,-2)$, $Y' (x,y) = (-5,1)$ and $Z'(x,y) = (2,-3)$.