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: $|c_2-c_1|/√(m^2+1)$.

 


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