Warm Up Find the equation of the line that goes through the points (-1, 2) and (2, 5). Find the equation of the line perpendicular to the line you found that goes through the point (0,2). Find the value of r if the slope of the line through points (r, 0) and (3, 4) is 2.

Perpendiculars and Distance Section 3.6 Perpendiculars and Distance

Distance between a Point and a Line

Perpendicular Postulate

Example 1 a) A certain roof truss is designed so that the center post extends from the peak of the roof (point A) to the main beam. Construct and name the segment whose length represents the shortest length of wood that will be needed to connect the peak of the roof to the main beam.

Example 1 b) Which segment represents the shortest distance from point A to segment DB

Example 2 a) Line s contains points at (0, 0) and (–5, 5). Find the distance between line s and point V(1, 5).

Example 2 b) Line n contains points (2, 4) and (–4, –2). Find the distance between line n and point B(3, 1). B(3, 1) (2, 4) (–4, –2)

Equidistant By definition, parallel lines do not intersect. An alternate definition states that two lines in a plane are parallel if they are everywhere equidistant. Equidistant means that the distance between two lines measured along a perpendicular line to the lines is always the same. This leads to the definition of the distance between two parallel lines.

Example 3 a) Find the distance between the parallel lines a and b whose equations are y = 2x + 3 and y = 2x – 1, respectively.

Example 3 b) Find the distance between the parallel lines a and b whose equations are and , respectively.