1. Lesson 3-6: Perpendicular & Distance
TARGETS
Find the distance between a point and a line.
Find the distance between parallel lines.
Target

2. Perpendicular Postulate
LESSON 3-6: Perpendicular Distance
Perpendicular Postulate
If given a line and a point not on the line,
then there exists only one line through the point
that is perpendicular to the given line
Perpendicular Postulate

3. Distance Between a Point & a Line
LESSON 3-6: Perpendicular Distance
Distance Between a Point and a Line
The distance between a line and a point not on
the line is the length of the segment perpendicular
to the line from the point.
Distance Between a Point & a Line

4. Step 1 Write an equation for the given line
LESSON 3-6: Perpendicular Distance
EXAMPLE 2
Distance from a Point to a Line on Coordinate Plane
COORDINATE GEOMETRY Line s contains points at (0, 0) and (–5, 5). Find the distance between line s and point V(1, 5).
Step 1 Write an equation for the given line
Step 2 Write an equation for the
perpendicular line to line s through V(1, 5).
Example 2

5. Step 3 Solve the system of equations to
LESSON 3-6: Perpendicular Distance
EXAMPLE 2
Distance from a Point to a Line on Coordinate Plane
COORDINATE GEOMETRY Line s contains points at (0, 0) and (–5, 5). Find the distance between line s and point V(1, 5).
Step 3 Solve the system of equations to
determine the point of intersection.
Example 2

6. Step 4 Use the Distance Formula to
LESSON 3-6: Perpendicular Distance
EXAMPLE 2
Distance from a Point to a Line on Coordinate Plane
COORDINATE GEOMETRY Line s contains points at (0, 0) and (–5, 5). Find the distance between line s and point V(1, 5).
Step 4 Use the Distance Formula to
determine the distance between Z(–2, 2)
and V(1, 5).
Example 2

7. Example 2 additional problem
LESSON 3-6: Perpendicular Distance
EXAMPLE 2
Distance from a Point to a Line on Coordinate Plane
COORDINATE GEOMETRY Line n contains points (2, 4) and (–4, –2). Find the distance between line n and point B(3, 1).
Example 2 additional problem

8. Lesson 3-6: Perpendicular & Distance
TARGETS
Find the distance between a point and a line.
Find the distance between parallel lines.
Target

9. Distance Between Parallel Lines
LESSON 3-6: Perpendicular Distance
Distance Between Parallel Lines
The distance between two parallel lines is the
perpendicular distance between one of the lines and any point on the other line.
Distance Between Parallel Lines

10. Step 2 Solve the system of equations to find the point of intersection
LESSON 3-6: Perpendicular Distance
EXAMPLE 3
Distance Between Parallel Lines
COORDINATE GEOMETRY Find the distance between the parallel lines a and b whose equations are y = 2x + 3 and
y = 2x – 1, respectively. a b
Step 1 Write an equation for a line that is perpendicular to lines a & b; call this
line p
Step 2 Solve the system of equations to
find the point of intersection
Example 3 (Steps 1 & 2)

11. LESSON 3-6: Perpendicular Distance
EXAMPLE 3
Distance Between Parallel Lines
COORDINATE GEOMETRY Find the distance between the parallel lines a and b whose equations are y = 2x + 3 and
y = 2x – 1, respectively.
Step 3 Use the Distance Formula to determine the distance between the two parallel lines a b
Example 3 (Step 3)

12. Example 3 additional problem
LESSON 3-6: Perpendicular Distance
EXAMPLE 3
Distance Between Parallel Lines
COORDINATE GEOMETRY Find the distance between the parallel lines a and b whose equations are x + 3y = 6 and, x + 3y = -4, respectively.
Example 3 additional problem