what is the rule used to transform $\triangle abc$ to its image?\n$a(-3,5), b(2,8), c(-4,-5)$ and $a(-3,-5)…

what is the rule used to transform $\triangle abc$ to its image?\n$a(-3,5), b(2,8), c(-4,-5)$ and $a(-3,-5), b(2,-8), c(-4,5)$\na. $r_m(x,y)=(-y,-x)$, where the equation of line $m$ is $y = -x$\nb. $r_n(x,y)=(y,x)$, where the equation of line $n$ is $y = -x$\nc. $r_{y - axis}(x,y)=(-x,y)$\nd. $r_{x - axis}(x,y)=(x,-y)$

what is the rule used to transform $\triangle abc$ to its image?\n$a(-3,5), b(2,8), c(-4,-5)$ and $a(-3,-5), b(2,-8), c(-4,5)$\na. $r_m(x,y)=(-y,-x)$, where the equation of line $m$ is $y = -x$\nb. $r_n(x,y)=(y,x)$, where the equation of line $n$ is $y = -x$\nc. $r_{y - axis}(x,y)=(-x,y)$\nd. $r_{x - axis}(x,y)=(x,-y)$

Answer

Explanation:

Step1: Analyze the coordinate - change pattern

Given (A(-3,5)) and (A'(-3, - 5)), (B(2,8)) and (B'(2,-8)), (C(-4,-5)) and (C'(-4,5)). The (x) - coordinates of the original points and their images remain the same, while the (y) - coordinates change their signs.

Step2: Recall transformation rules

The transformation rule for reflection over the (x) - axis is (r_{x - axis}(x,y)=(x,-y)).

Answer:

D. (r_{x - axis}(x,y)=(x,-y))