Algebra 2

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Algebra 2

• Chapter 9 Conic Sections Circles and Parabolas

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9-1 Distance and Midpoint Formulas

• WARMUP
• Simplify
• -5 2 5.
• ( -1 (-4))2
• -2 (-6)
• (3 (-5))2 ( -4 - 2)2

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9-1 Distance and Midpoint Formulas

• Objective To find the distance between any two
  points and the midpoint of the line segment
  joining them.

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9-1 Distance and Midpoint Formulas

• Chapter 9 has a subtitle of Conic Sections.
• http//clem.mscd.edu/talmanl/HTML/ConicSections.h
  tml

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9-1 Distance and Midpoint Formulas

• How do we tell the distance between any two
  points on a number line?

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9-1 Distance and Midpoint Formulas

• The distance between any two points P and Q is
  written PQ. On a number line, PQ is the
  absolute value of the difference between their
  coordinates.
• Since a b b a order doesnt
  matter.
• Example

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9-1 Distance and Midpoint Formulas

• What about two points in a coordinate plane?
• Pick two points

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9-1 Distance and Midpoint Formulas

• Reminder
• Pythagorean Theorem
• If the length of the hypotenuse of a right
  triangle is c, and the lengths of the other two
  sides (legs) are a and b, then

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9-1 Distance and Midpoint Formulas
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9-1 Distance and Midpoint Formulas

• The Distance Formula
• The distance between the points
  and is

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9-1 Distance and Midpoint Formulas

• Find the distance between
• points ( -2, -1 ) and ( -4, 3 )
• points ( 2, -7 ) and ( 2, -1 )

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9-1 Distance and Midpoint Formulas

• The distance formula can be used to prove the
  Midpoint Formula
• The Midpoint Formula
• The midpoint (M) of the line segment joining
• and is

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9-1 Distance and Midpoint Formulas

• Find the midpoint of the line segment joining the
  points
• ( 4, -6 ) and ( -3, 2 )
• ( 7, 5 ) and ( -1, -3 )

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9-1 Distance and Midpoint Formulas

• Typical test question
• Find the coordinates of Q given that M is the
  midpoint of the line segment PQ
• P( 0, 0 ), M( 3, 5 )
• Can do it graphically. On a test you MUST do it
  mathematically

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9-1 Distance and Midpoint Formulas
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9-1 Distance and Midpoint Formulas

• More examples

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9-1 Distance and Midpoint Formulas

• Homework