21. Plane coordinate geometry
In a Euclidean x-y plane, the distance between two points \$(x_1,y_1)\$ and \$(x_2,y_2)\$ is given by \$√{(x_1-x_2)^2+(y_1-y_2)^2}\$.
This is called the Euclidean distance.

If a Line L intersects the x and y axes at points P and Q respectively, with origin O, then, length OP is called the x intercept, and length OQ is called the y intercept.
The slope \$m\$ of a line passing through \$(x_1,y_1)\$ and \$(x_2,y_2)\$ is given by: \$m={(y_2-y_1)}/{(x_2-x_1)}\$
The equation of a line is given by \$y=mx+c\$ where \$m\$ is the slope, and \$c\$ is the y-intercept.
This form of the line equation is called the slope intercept form.

Given the slope \$m\$ of a line L, and a point \$(x_1,y_1)\$ on it, its equation is \$(y-y_1)=m(x-x_1)\$.
Two lines with the same slope are parallel. Two lines with slopes \$m_1\$ and \$m_2\$ such that \$m_1m_2=-1\$ are perpendicular or intersect at right angles.

Given a line with x intercept \$a\$ and y intercept \$b\$, its equation is given by \$x/a+y/b=1\$.
This is called the two intercept form of the equation of the line.

The distance between two parallel lines \$y=mx+c_1\$ and \$y=mx+c_2\$ is given by: \$|c_2-c_1|/√(m^2+1)\$.