- Assume that
. Prove that the perpendicular distance from
to the line passing through the points
and
is given by the formula
- Compute the distance in the case
- Proof. We know the area of the parallelogram determined by
and
is given by
But this is exactly twice the area of the triangle with base
and height the perpendicular line from
to the line through
and
. Hence,
is the perpendicular distance from
to the line through
and
, and
- When
we have
there is a typo in first exercise. it is B-C not B-A