5'5 Coordinate Geometry

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5.5 Coordinate Geometry
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Problem of the Day

• What type of polygon am I? My opposite angles
  have equal measures. My consecutive angles are
  supplementary. I do not have right angles. All
  my sides are congruent.
• Answer Rhombus

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Slope

• Slope is rise over run
• Slope m rise run
• Slope is the steepness
• of a line.

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Slope

• Run is left to right.
• Like a runner.
• This is the x-axis
• Rise is up and down.
• Like a hot air balloon
• rises and falls.
• This is the y-axis.

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Example

• Find the slope of this line.
• m rise 4 2 run 2 1
• The slope of the line is 2.

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Positive Slope

• A positive slope is when the line rises.
• like a hill you have to walk up
• m is also a positive number

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Negative Slope

• A negative slope is when the line decreasing
  downward.
• like a hill your walking down
• m is also a negative number

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Positive and Negative Slope

• Remember
• Positive people bring you up, and negative
  people bring you down.
• Same applies to positive and negative
  slopes. Positive slope go up, and negative
  slopes go down.

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Slope of 0

• A line has a slope of 0 if it is a horizontal
  line.
• This is because
• m rise 0 0 run 3
• Remember a 0 in
• the numerator always
  equals 0.

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Undefined Slope

• A line has an undefined slope if it is a vertical
  line.
• This is because
• m rise 3
  run 0
• undefined slope
• Remember a 0 in the
• denominator always
• gives you an undefined number.

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Types of Slopes




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Parallel Lines

• What is the slope of each line?
• Line A
• m 2 1
• 6 3
• Line B
• m 2 1
• 6 3
• Parallel lines have the same slope.

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Perpendicular Lines

• What is the slope of each line?
• Line A
• m - 4
• 3
• Line B
• m 3
• 4
• Perpendicular lines have opposite reciprocal
  slopes.

(2, 0)
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Group Activity

• Find a quadrilateral that has sides AB parallel
  to CD, AB perpendicular to CB, and CB cannot be
  parallel to AD. Then, find the slope of each
  side of the quadrilateral.
• You can have your picture whichever way you like,
  but you must follow the instructions above.

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Group Activity
Slope rise 2 1 run 2
1

• Answer

(2, 4)
Vertical line Slope undefined
Vertical line Slope undefined
Horizontal line Slope 0
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Homework

• Page 246-247
• 1-16