Reflect the Shape A in the line x = 1. I'm not that sure on how to reflect the Shape $A$. I know where the line $x = 1$ but I don't know which way to reflect it. To the left or up? Thanks, I know it seems a bit easy.

 A: If you were to fold the graph on the line you're reflecting through, the original shape and the reflected shape should line up exactly.
This could apply to any line: vertical, horizontal or otherwise.
A: To reflect anything around a line, as was pointed out by @rscwieb, makes the mirror image appear on the other side of the line. (Mirror image means an inverted shape).
Reflecting around $x=1$ never touches the $y$ coordinate, and the $x$ coordinate transforms - what was the distance to $x=1$ becomes the distance on the other side. In other words, if a point were at $x = \pi$, it's distance to $x=1$ was $\pi - 1$ so the new location is $\pi - 1$ to the left of $x=1$, i.e. $1- (\pi-1) = 2 - \pi$.
This gives you the idea, now try it yourself on the figure you drew.
A: *

*Subtract 1 from x-coordinates.

*Switch sign of x-coordinates.

*Add 1 to x-coordinates.
You can do all this with the matrix operations:
$$\begin{bmatrix}1&0&1\\0&1&0\\0&0&1\end{bmatrix} \begin{bmatrix}-1&0&0\\0&1&0\\0&0&1\end{bmatrix} \begin{bmatrix}1&0&-1\\0&1&0\\0&0&1\end{bmatrix}$$
You then multiply with this matrix from the right:
$$\begin{bmatrix}{\bf x}^T\\{\bf y}^T\\{\bf 1}^T\end{bmatrix}$$
$\bf x$ being column vector of x-coordinates
$\bf y$ being column vector of y-coordinates
$\bf 1$ being column vector of the value 1.
