Perpendicular

Perpendicular

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┴Perpendicular lines are lines that Perpendicular lines are lines that intersect in a right angle.intersect in a right angle.

┴The slopes of perpendicular lines are The slopes of perpendicular lines are negative reciprocals of each other. negative reciprocals of each other. (Multiplying the two slopes together (Multiplying the two slopes together & their product will equal –1.)& their product will equal –1.)

┴Find the equation of a perpendicular: Find the equation of a perpendicular: a.) first find the a.) first find the slope (slope (m)m) of the given line; of the given line;

b.) find the equation of the line b.) find the equation of the line through the given point with opposite through the given point with opposite reciprocal slope.reciprocal slope.

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1Are the lines 2 5 and 4 perpendicular?

2x y y x

Find the slope of 2 5 2

2 5

x y m

y x

1 1Find the slope of 4

2 2y x m

Since the slopes are negative reciprocals of each other the lines are perpendicular.

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The red line is the graph of y = – 2x + 5

and the blue line is the graph ofy = – 1/2 x +4

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r6 3 5

3 6 5

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x y

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Are the lines 6 3 5 and 2 4 4 perpendicular?x y y x

2 4 4

2 2

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y x

m

Since the slopes are not negative reciprocals of each other (their product is not -1) the lines are not perpendicular

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Are the lines 2 4 and 4 2 6 perpendicular?x y x y

2 4

2 4

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y x

y x

m

4 2 6

2 4 6

2 3

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x y

y x

y x

m

Since the slopes are negative reciprocals of each other (their product is -1) the lines are perpendicular.

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Find the equation of a line going through the point (3, -5) and perpendicular to 2 83y x

The slope of the perpendicular line will be m = 3/2.

┴Using the slope-intercept form of an equation where the slope m = 3/2 andthe point is (3, -5) we get…

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Find the equation of the line going through the point (4,1) and Perpendicular to 3 7y x

Find the equation of the line going through the point (-2,7) and perpendicular to 2 8x y

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