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To find the gradient of lines perpendicular to each other.
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Finding the Midpoint
1 2 3
6
9
5
8
4
7
Starter
(We’re going to use this later)
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These lines are perpendicular
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PERPENDICULAR PERPENDICULAR MEANSMEANS
AT RIGHT ANGLESAT RIGHT ANGLES
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What is each gradient?
21
Gradient = ½
2
1
Gradient = -2
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What is each gradient?
3
1
Gradient = 3
31
Gradient = -1/3
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THE GRADIENT OF A THE GRADIENT OF A PERPENDICULAR LINE IS THEPERPENDICULAR LINE IS THE
NEGATIVE RECIPROCALNEGATIVE RECIPROCALOF THE OTHEROF THE OTHER
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What is the gradient of the lines perpendicular to these?
y = 2x + 1
y = 3x + 2
y = 2 + 4x
y + 2x = 2
2y = 3x - 2
5y + 2x = 3
m = 2
m = 3
m = 4
m = -2
m = 3/2
m = -2/5
-1/m= -1/2
-1/m= -1/4
-1/m= -1/3
-1/m= 1/2
-1/m= -2/3
-1/m= 5/2
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Write down an equation of a line perpendicular to these:
y = 2x + 1
y = 3x + 2
y = 2 + 4x
y + 2x = 2
2y = 3x - 2
5y + 2x = 3
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THE PRODUCT OF GRADIENTS OFTHE PRODUCT OF GRADIENTS OFPERPENDICULAR LINES IS EQUAL PERPENDICULAR LINES IS EQUAL
TO -1TO -1
Exercise 5E Question 1
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Two points A(1,2) and B(-3,6) are joined to make the line AB.
Find the equation of the perpendicular bisector of AB