Geometry: For Enjoyment and Challenge 4.6 Slope Mike Beamish.

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Presentation transcript:

Geometry: For Enjoyment and Challenge 4.6 Slope Mike Beamish

Introduction When lines are drawn on a plane, their slant is referred to as the slope of the line. When lines are drawn on a plane, their slant is referred to as the slope of the line. Slope is a number that represents the change in the “y” coordinates and dividing this by the change in the “x” coordinates. Slope is a number that represents the change in the “y” coordinates and dividing this by the change in the “x” coordinates.

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

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

Rules Horizontal lines have zero slope Horizontal lines have zero slope

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

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

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

Example Example: Example: Given the diagram with triangle ABC. Find the slope of the altitude to BC, Find the length of the median to BC and find the slope of AD if it is parallel to BC. Given the diagram with triangle ABC. Find the slope of the altitude to BC, Find the length of the median to BC and find the slope of AD if it is parallel to BC. Slope of BC = 8/12 or 2/3 Slope of BC = 8/12 or 2/3 Slope of AN (altitude) = - 3/2 (negative reciprocal) Slope of AN (altitude) = - 3/2 (negative reciprocal) The coordinates of M are (11,9) so the Slope of AM = - 6/8 or - 3/4 The coordinates of M are (11,9) so the Slope of AM = - 6/8 or - 3/4 The slope of AD // BC = 2/3 since it must be the same. The slope of AD // BC = 2/3 since it must be the same.

Example #2

Works Cited Milauskas, George, Robert Whipple, and Richard Rhoad. Geometry: for Enjoyment and Challenge. New ed. Boston: McDougal Littell, Milauskas, George, Robert Whipple, and Richard Rhoad. Geometry: for Enjoyment and Challenge. New ed. Boston: McDougal Littell, Wing, Joan. "Chapter " Joan Wing Mathematics. 25 Aug May Wing, Joan. "Chapter " Joan Wing Mathematics. 25 Aug May 2008.