Lines (or
segments) are called
perpendicular if
their intersection with one another forms a
right angle. You can see for
yourself that if one of the
angles formed by the intersection of two lines
or segments is a right angle, then all four angles created will also be right
angles.
Figure 4.1: Perpendicular lines
Intersecting lines that are not
perpendicular to one another are called
oblique lines.
Through any given line, there are an infinite number of perpendicular lines.
Can you see why?
Figure 4.2: An infinite number of lines perpendicular to any given line
Through a specific
point on a line, though,
there exists only one perpendicular line. Likewise, given a line and a point
not on that line, there is only one perpendicular line through the
noncolinear point.
Figure 4.3: Perpendicular lines through a point on a line, and a point not on that
line
In the picture on the left, line AB contains the point C. There exists only one
line, line DE, that contains C
and is perpendicular to line AB. In the
picture on the right, point C is not on line AB. There exists only one line,
line CD, that contains C
and is perpendicular to line AB.
The Distance Between a Line and a Point not on that Line
When working with geometry it is a common problem to have to find the distance
between a line and a point not on that line. There are many different segments
that could be drawn between the point and the line, but when you need to find
the distance between the point and the line, it is implied that you are seeking
the shortest distance. This is found by drawing the segment through the
point which is perpendicular to the line, and taking its length. The
distance between a line and a noncolinear point is represented by this segment.
Figure 4.4: The distance between a line and a point not on that line
In this figure, the shortest distance between the point C and the line AB is
along the segment CD, which is perpendicular to the line AB.
