Basic results and techniques

If P1 ≡ (x1, y1) and P2 ≡ (x2, y2), we obtain the following results directly from Fig. 1.1. $$Dis\tan ce\;{P_1}{P_2}\quad \quad \surd \left[ {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} \right].$$ (1.1) $$Gradient\;of\,{P_1}{P_2}\quad \quad \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}.$$ (1.2) $$Mid - po\operatorname{int} \;of\;{P_1}{P_2}\quad \quad \left( {\frac{{{x_1} - {x_2}}}{2},\frac{{{y_1} - {y_2}}}{2}} \right).$$ (1.3) $$\begin{array}{*{20}{c}} {Equation\;of\;{P_1}{P_2}\quad \quad y - {y_1} = m\left( {x - {x_1}} \right)} \\ { \equiv y \equiv mx + c,} \end{array}$$ (1.4) where m = (y2 − y1)/(x2 − x1), and c = y1 − mx1.