10.1 The Distance and Midpoint Formulas

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10.1 The Distance and Midpoint Formulas
What you should learn
Goal
1
Find the distance between two points and find the
midpoint of the line segment joining two points.
Goal
2
Classify a Triangle.
Goal
3
Write an equation for a perpendicular bisector of
a line segment.
10.1 The Distance and Midpoint Formulas
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Geometry Review!

• What is the difference between the symbols AB and
  AB?

Segment AB
The length of Segment AB
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The Distance Formula
Goal
1

• The Distance d between the points (x1,y1) and
  (x2,y2) is

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Pythagorean Formula A2 b2 c2 or c v(a2 b2)
C
B
A
How long is a?
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How long is b?
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How long is c?
5.7
A x2 x1 and B y2 y1
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Find the distance between the two points.

• (-2,5) and (3,-1)
• Let (x1,y1) (-2,5) and (x2,y2)
  (3,-1)

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Classify the Triangle using the distance formula
(as scalene, isosceles or equilateral)
Goal
2
Because ABBC the triangle is ISOSCELES
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The Midpoint Formula

• The midpoint between the two points (x1,y1) and
  (x2,y2) is

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Find the midpoint of the segment whose endpoints
are (6,-2) (2,-9)
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Write an equation in slope-intercept form for the
perpendicular bisector of the segment whose
endpoints are C(-2,1) and D(1,4).
Goal
3

• First, find the midpoint of CD.
• (-1/2, 5/2)
• Now, find the slope of CD.
• m1
• Since the line we want is perpendicular to the
  given segment, we will use the opposite
  reciprocal slope for our equation.

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(y-y1)m(x-x1) or ymxb Use (x1
,y1)(-1/2,5/2) and m-1 (y-5/2)-1(x1/2) or
5/2-1(-1/2)b y-5/2-x-1/2 or
5/21/2b y-x-1/25/2 or 5/2-1/2b y-x2
or 2b y-x2
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Assignment