First Principles AI

Solution

Reflection over the $y$ -axis maps:

(x,y)\mapsto (-x,y)

The transformation matrix is:

R=\begin{bmatrix}-1&0\\0&1\end{bmatrix}

Given:

A(4,1),\quad B(-2,5),\quad C(0,-3)

Compute:

A'=R\begin{bmatrix}4\\1\end{bmatrix}=\begin{bmatrix}-4\\1\end{bmatrix}\Rightarrow A'(-4,1)

B'=R\begin{bmatrix}-2\\5\end{bmatrix}=\begin{bmatrix}2\\5\end{bmatrix}\Rightarrow B'(2,5)

C'=R\begin{bmatrix}0\\-3\end{bmatrix}=\begin{bmatrix}0\\-3\end{bmatrix}\Rightarrow C'(0,-3)

\boxed{A'(-4,1),\; B'(2,5),\; C'(0,-3)}