P'5 The Cartesian Plane

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P.5The Cartesian Plane

• Our goals are to learn
• How to plot points in the Cartesian Plane
• Use the distance formula to find the distance
  between two points.
• Use the Midpoint formula to find the midpoint of
  a line segment.
• Find the equation of a circle.
• Translate points in the plane
• Why do you need to know this?
• For something as common as MAP-READING

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The Cartesian Plane

• An ordered pair is . . . a pair of two real
  numbers x and y, written (x, y), which represents
  a point in the Cartesian plane.

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ExamplesPlot the ordered pairs on the coordinate
plane.

• (4, -2), (0, 0), (-4, 0), (-5, -5)

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ExampleFind the coordinates of the point

• The point is located three units below the x-axis
  and two units to the right of the y-axis.
• The point is on the x-axis and 10 units to the
  left of the y-axis.

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ExampleDetermine the quadrant(s) in which (x, y)
is located so that the condition(s) is (are)
satisfied.

• xlt0 and ylt0
• x -4 and y gt 0
• x gt 4
• -x gt 0 and y lt 0
• xy lt 0

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Practice Time!

• Now try problems 67 and 69 on your handout.

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Use the distance formula to find the length of
the segment.

• (6, -3), (6, 5)
• (-3, -1), (2, -1)
• (8, 5), (0, 20)

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Practice Time!

• Now try problem 70 on your handout.

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ExamplesFind the length of each side of the
right triangle and show that these lengths
satisfy the Pythagorean Theorem.
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ExamplesShow that the points form the vertices
of the polygon

• Parallelogram (0, 1), (3, 7), (4, 4), (1, -2)

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Practice Time!

• Now try problems 70 and 72 on your handout.

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Use the midpoint formula to find the center of
the segment.

• (6, -3), (6, 5)
• (-3, -1), (2, -1)
• (8, 5), (0, 20)

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Practice Time!

• Now try problems 74-75 on your handout.

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The equation of a circle

• You need to know the standard form of the
  equation of a circle with Center (h, k) and
  radius, r
• Write the standard form of the equation of the
  specified circle
• Center (0, 0) radius 5
• Center (5, -6) radius
• Center (3, -2) solution point (-1, 1)
• Endpoints of a diameter (-4, -1), (4, 1)

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Find the center and radius, and sketch the circle.
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Practice Time!

• Now try problems 76-78 on your handout.