section 3.1 parallel and perpendicular lines. map tap 2003-2004parallel and perpendicular lines 2...
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Section 3.1 Parallel and Perpendicular Lines
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Parallel Lines – lie on same plane and never intersect
Perpendicular Lines – intersects to form a right angle
Skew Lines – do not lie on the same plane, never intersects
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Parallel Lines (Algebra Review)
Two non-vertical lines are parallel if and only if their slopes are equal. If l1║l2, then m1= m2.
If m1= m2, then l1║l2.
l1 l2
m1 m2
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Write the equation of the line that passes through (3,6) and is parallel to y = 2/3x+2.
m = 2/3 and the point is (3,6)
y = mx+b
6 = 2/3(3)+b
6 = 2+b
4 = b
y = 2/3x+4
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Write the equation of the line that passes through (4,-5) and is parallel to y = -2x-4.
m = -2 and the point is (4,-5)
y = mx+b
-5 = -2(4)+b
-5 = -8+b
3 = b
y = -2x+3
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Write the equation of the line that passes through (-6,4) and is parallel to y=1/3x-1.
m=1/3 and the point is (-6,4)
y =1/3x+6
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Perpendicular Lines (Algebra Review)
Two non-vertical lines are perpendicular if and only if the product of their slopes is -1. If l1┴l2, then m1 ● m2= -1.
If m1● m2 = -1, then l1┴l2.l1
l2
m2m1
Slopes are negative reciprocals
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Write the equation of the line that passes through (6,-5) and is perpendicular to y = 2x+3.
m = -1/2 and the point is (6,-5)
y = mx+b
-5 = -1/2(6)+b
-5 = -3+b
-2 = b
y = -1/2x-2
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Write the equation of the line that passes through (6,-7) and is perpendicular to y = 2/3x+1.
m = -3/2 and the point is (6,-7)
y = mx+b
-7 = -3/2(6)+b
-7 = -9+b
2 = b
y = -3/2x+2
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Write the equation of the line that passes through (-4,-3) and is perpendicular to y = x+6.
m = -1 and the point is (-4,-3)
y = -x-7
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What’s going on in this graph?
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skew lines can exist only in three or more dimensions.
Skew Lines
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Which lines are skew?
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What’s going on here?
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Which lines are parallel?
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Main Idea
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Over head examples
In-Class practice problems
Homeworkp110-111 #1-19 & 25-29