Chapter 3-6 Perpendiculars and Distance

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Presentation transcript:

Chapter 3-6 Perpendiculars and Distance

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

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

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

Find the distance between the parallel lines

Graph the original two equations.

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

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

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)

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

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