Geometry:Geometry:For Enjoyment and For Enjoyment and

ChallengeChallenge4.64.6

SlopeSlope

Mike BeamishMike Beamish

IntroductionIntroduction

When lines are drawn When lines are drawn on a plane, their on a plane, their slantslant is referred to as the is referred to as the slope of the line.slope of the line.

Slope is a number Slope is a number that represents the that represents the change in the “y” change in the “y” coordinates and coordinates and dividing this by the dividing this by the change in the “x” change in the “x” coordinates. coordinates.

Positive SlopesPositive Slopes

Lines that slope up and to the right Lines that slope up and to the right have a positive slope. have a positive slope.

Negative SlopesNegative Slopes

Lines that slope down to the right Lines that slope down to the right have negative slopes have negative slopes

RulesRules

Horizontal lines Horizontal lines have zero slopehave zero slope

RulesRules

Vertical lines have Vertical lines have NO slope.NO slope.

RulesRules

To test if lines are parallel, make To test if lines are parallel, make sure they have the same slope. sure they have the same slope.

RulesRules

To test if lines are perpendicular, check to To test if lines are perpendicular, check to see if their slopes are negative reciprocals.see if their slopes are negative reciprocals.

ExampleExample Example:Example: Given the diagram with Given the diagram with

triangle ABC.  Find the triangle ABC.  Find the slope of the altitude to BC, slope of the altitude to BC, Find the length of the Find the length of the median to BC and find the median to BC and find the slope of AD if it is parallel slope of AD if it is parallel to BC.to BC.

Slope of BC = 8/12 or 2/3Slope of BC = 8/12 or 2/3 Slope of AN (altitude) = -Slope of AN (altitude) = -

3/2  (negative reciprocal)3/2  (negative reciprocal) The coordinates of M are The coordinates of M are

(11,9) so the Slope of AM = (11,9) so the Slope of AM = -6/8 or - 3/4-6/8 or - 3/4

The slope of AD // BC = 2/3 The slope of AD // BC = 2/3 since it must be the same.  since it must be the same.  

Example #2Example #2

Works CitedWorks Cited Milauskas, George, Robert Whipple, and Richard Rhoad. Milauskas, George, Robert Whipple, and Richard Rhoad.

Geometry: Geometry: for Enjoyment and Challengefor Enjoyment and Challenge. New ed. . New ed.

Boston: McDougal Boston: McDougal Littell, 1996. 198-202.Littell, 1996. 198-202.

Wing, Joan. "Chapter 4-2000." Wing, Joan. "Chapter 4-2000." Joan Wing MathematicsJoan Wing Mathematics. 25 . 25 Aug. Aug. 2002. 29 May 2008 2002. 29 May 2008 <http://teacherweb.ftl.pinecrest.edu/wi <http://teacherweb.ftl.pinecrest.edu/wi ngjoa/Myngjoa/My%20Webs/Geometry/Chapter %204.htm>. %20Webs/Geometry/Chapter %204.htm>.