Prove that the distance from the point $(x_0,y_0)^T$ to the line ax + by = 0 is $\frac{|ax_0 + by_0|}{\sqrt{a^2 +b^2}}$, also what is the minimum distance to the line ax + by + c = 0?
My attempt:
$\left( \left( \begin{matrix} x_0 \\ y_0 \end{matrix} \right) - c \left( \begin{matrix} a/b \\ -a/b \end{matrix} \right) \right) . \left( \begin{matrix} a/b \\ -a/b \end{matrix} \right) = 0$ so $\frac{\left( \begin{matrix} x_0 \\ y_0 \end{matrix} \right) . \left( \begin{matrix} a/b \\ -a/b \end{matrix} \right)}{\left( \begin{matrix} a/b \\ -a/b \end{matrix} \right). \left( \begin{matrix} a/b \\ -a/b \end{matrix} \right)} . \left( \begin{matrix} a/b \\ -a/b \end{matrix} \right) = \left( \begin{matrix} \frac{a}{b}(x_0 - y_0) \\ \frac{2a^2}{b} \end{matrix} \right)$ , but how can I complete this to match the the answer given in the question. Also, I do not know how to do part II of this problem.