# A triangle has corners at (3, -5 ), ( 2 , -1), and ( 4 , 3). What will the new coordinates of the triangle be if it is reflected across the x-axis?

Jul 29, 2016

$\left(3 , - 5\right) \to \left(3 , 5\right) , \left(2 , - 1\right) \to \left(2 , 1\right) , \left(4 , 3\right) \to \left(4 , - 3\right)$

#### Explanation:

Under a reflection in the x-axis a point

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\left(x , y\right) \to \left(x , - y\right)} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Under a reflection in the y-axis a point

color(red)(|bar(ul(color(white)(a/a)color(black)((x,y)to(-x,y)color(white)(a/a)|)))#

$\Rightarrow \left(3 , - 5\right) \to \left(3 , 5\right) , \left(2 , - 1\right) \to \left(2 , 1\right) \text{ and } \left(4 , 3\right) \to \left(4 , - 3\right)$