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Contents
Perpendicular Lines
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Perpendicular
Lines
Given
two lines
l1 : y = m1x + c1
l2 : y = m2x + c2
If
l1 is perpendicular to l2, then
m1m2
= -1Proof:
 From
diagram,
m1 = tan q
q
+ a
= 90o
a
= 90o - q
m2 = tan (180o - a)
= tan [180o - (90o - q)]
= tan (90o + q)
= -cot q
complementary
angles
m1m2 = tan q
(-cot q)
= -1
Perpendicular
Bisector:
1.The
perpendicular bisector of a line segment is the equation of a line
perpendicular to the original segment and passing through the midpoint.
2.
The diagonals of the following quadrilaterals bisect each other
perpendicularly: squares and rhombuses.
 Example: Find
the perpendicular bisector of the line segment joining A (-2, 4) and B (5,
-3).
Solution:Gradient
of AB = (4+3)/(-2-5) = -1
Gradient
of perpendicular bisector = -1/-1 = 1
Midpoint
of AB = ([-2+5]/2, [4-3]/2) = (3/2, 1/2)
Equation:
y - 1/2 = x - 3/2
y = x - 1
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