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

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

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

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

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

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

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

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

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

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)

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)

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