1. Chapter 3-6 Perpendiculars and Distance

2. Distance between a Point and a Line:
The distance between a point and a line, is the
length of the segment perpendicular to the line
from the point. C
Shortest
distance B A

3. Which segment in the diagram represents the distance from R to XY?
___ A B C D RY RX MX RM

4. Equidistant: same distance.
Theorem:
In a plane if two lines are equidistant from
a third line, then the two lines are parallel
to each other.
If the distance
between line a
and b is d and
distance between
b and c is d
then a and c are
Parallel. d a b c

5. Find the distance between the parallel lines

6. Graph the original two equations.

7. Use to find the equation of
the line perpendicular to the original two equations.
Use one of the y intercepts of the original equations.
So the equation of the green
line is

8. Use system of equations to determine where the
green line intersects the top blue equation. =

9. The intersection point is (1,0)
Now you know that at x=1 the green graph
crosses the graph on top, plug in x=1 into the
equation of the green line.
The intersection point is (1,0)

10. Now use the distance formula:
Between points (0,-3) and (1,0).