Calculate the slope of a line passing through the intersection of two lines Let say I have this figure,

I know slope $m_1$, slope $m_1$, $(x_1, y_1)$, $(x_2, y_2)$ and $(x_3, y_3)$. I need to calculate slope $m_3$. Note the line with $m_3$ slope will always equally bisect line with $m_1$ slope and line with $m_2$.



We understand that:
    $$m_1=\tan(\alpha)$$
    $$m_2=\tan(\beta),$$
    Then:
    $$
m_3=\tan\left(\frac{\alpha+\beta}2\right).
$$


