Distance

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Distance Midpoint Formulas

• Sections covered
• 1.8 The Coordinate Plane

2
Review Coordinate Plane
3
Algebra Review

• Evaluate the expression for m -3 and n 7.

4
Algebra Review

• Evaluate the expression for m -3 and n 7.

5
Algebra Review

• Evaluate the expression for m -3 and n 7.

6
Algebra Review

• Evaluate the expression for a 6 and b -8.

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Algebra Review

• Evaluate the expression for a 6 and b -8.

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Simplifying Radicals
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Simplifying Radicals
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Simplifying Radicals
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Simplifying Radicals
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Distance Formula
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Example 1

• Find the distance between T(5,2) and R(-4,-1) to
  the nearest tenth.

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Example 2

• Find the distance between A(-1,5) and B(0,4).
  Leave in simplest radical form.

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Example 3

• Each morning Juanita takes the Blue Line subway
  from Oak Station to Jackson Station. Oak Station
  is 1 mile west and 2 miles south of City Plaza.
  Jackson Station is 2 miles east and 4 miles north
  of City Plaza. Find the distance Juanita travels
  between the two stations.

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The Midpoint Formula
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Example 4

• QS has endpoints Q(3,5) and S(7,-9). Find the
  coordinates of its midpoint M.

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Example 5

• Find the midpoint of segment EF, with E(-7,0) and
  F(5,8).

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Example 6

• The midpoint of AB is M(3,4). One endpoint is
  A(-3,-2). Find the coordinates of the other
  endpoint B.

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Example 7

• GH has endpoints G(-3,2) and H(3,-2). Find the
  coordinates of its midpoint.

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End of Notes

• Please pick up a whiteboard, a marker, and an
  eraser.

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Example 8

• On your whiteboard, graph the following points
• A(2,1), B(6,-1), C(8,7), D(4,9)
• Draw quadrilateral ABCD.
• Use the Midpoint Formula to find the midpoints of
  each side.
• What appears to be true?

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Example 9

• A boat at the point X(5,-2) needs to travel to
  Y(-6,9) or Z(17,-3). Which point is closer?
• What is the distance to the closer point?