A **point** is an ordered pair of real
numbers.

The **plane** is the set of all ordered
pairs of real numbers.

The **distance** between (*x*_{1},
*y*_{1}) and (*x*_{2}, *y*_{2}) is denoted by

and is defined to be

Two points are **vertical** if they have
the same *x-*coordinates.

Two points are **horizontal** if they
have the same *y-*coordinates.

A rational expression with a zero
denominator and a nonzero numerator has a value of
**infinity**.^{1}

The **slope** between (*x*_{1},
*y*_{1}) and (*x*_{2}, *y*_{2}) is

A **line** is the set of all
points whose coordinates are solutions to a
linear equation in two
unknowns.^{2}

The **slope of a line** is the slope
between any two points on the
line.^{3}

A **vertical line** is one where
all of the points are vertical

A **horizontal line** is one
where all the points are horizontal.

The **point-slope form of the equation**
of the line through (*x*_{1}, *y*_{1}) with slope *m *is

Two lines are **parallel** if their
slopes are the same.

Two lines are **perpendicular** if
their slopes are negative reciprocals of each
other.^{4}

Given a line and a
point, the point where the
line through the given point
perpendicular to the given
line intersects the given
line is called the **foot** of the
point in the line.