100 likes | 237 Views
Geometry. 3.6 Perpendiculars and Distance. 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. Postulate 3.6 Perpendicular Postulate.
E N D
Geometry 3.6 Perpendiculars and Distance
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.
Postulate 3.6Perpendicular Postulate • If given a line and a point not on the line, then there exists exactly one line through the point that is perpendicular to the given line.
Ex. 1 • Copy the figure and construct the segment that represents the distance from Q to segment RS. S R Q P
Steps to find distance if given a line and a point • 1) Find the equation for the given line. • 2) Write an equation for line perpendicular to the given line through the given point. • 3) Find the point of intersection between the two lines. • 4) Use the distance formula to find the distance between the given point and intersection.
Example 2 • Line s contains points (0,0) and (-5,5). Find the distance between line s and point V(1,5)
The distance between two parallel lines is the perpendicular distance between one of the lines and any point on the other line. • Theorem 3.9: In a plane, if two are lines are equidistant from a third line, then the two lines are parallel to each other.
Steps to find distance between two parallel lines. • 1. Write an equation for a line perpendicular to the parallel lines. Use the same y-intercept as a given line. • 2. Solve a system of equation to find the perpendicular line intersects the other line. • 3. Use the distance formula to find the distance between the points of intersection.
Example 3 • Find the distance between the parallel lines a and b with equations y= 2x +3 and y =2x -1
Homework • Page 218: 9-27 odds