8.1 The Rectangular Coordinate System and Circles

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8.1 The Rectangular Coordinate System and Circles

• Part 1 Distance and Midpoint Formulas

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Rectangular Coordinates

• A pair of numbers in the form (x , y) is an
  example of an ordered pair.
• The numbers in an ordered pair are
  the
  components of the ordered pair.
• An ordered pair is plotted (or
  
  graphed) on a rectangular (or
  Cartesian)
  coordinate system.
• The axes from four quadrants.
  (A
  point on an axis is not
  considered to be
  in any quadrant.)

y-axis
IV
I
x-axis
origin
II
III
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Distance Formula

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

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Finding the Distance Between Two Points

• Find the distance between (-3, 5) and (6, 4).

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?Find the distance between (3, 4) and (-2, 1).
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Midpoint Formula

• The midpoint of a line segment is the point on
  the segment that is equidistant from both
  endpoints.
• Given the coordinates of the two endpoints of a
  line segment, we can find the midpoint by
  averaging the coordinatesor by using

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Finding the Midpoint of a Segment

• Find the coordinates of the midpoint of the line
  segment with endpoints (8, -4) and (-9, 6).

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?Find the coordinates of the midpoint of the line
segment with endpoints (3, 4) and (-2, 1).
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Graphing in the Third Dimension(NOT in the book!)

• A 3-dimensional graph has a z-axis along with the
  x- and y-axis, so points have 3 coordinates (x,
  y, z).
• 3-D Distance Formula
• 3-D Midpoint Formula