axiom

the midpoint of the two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

two lines are parallel if their gradients are equal

two lines are perpendicular if their gradients multiply to get -1