May 14, 2014

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May 14, 2014

  1. 1. Today Make-Up Tests?  Khan Academy Review  Review for Friday’s Test  New Material: Distance & Mid-Point Formulas Class Work May 14
  2. 2. Warm-Up
  3. 3. Khan Academy: Radical Equations
  4. 4. Khan Academy: Pythagorean Theorem 81 – 26 = 𝟓𝟔 = 7.48 A building is on fire and you need to set the ladder back 10 ft. to prevent burning. What is the shortest ladder (in feet) that will reach the third story window ? What is the perimeter of the sail?
  5. 5. Test Review: Radical Operations: (4) The problems on Friday’s test aren’t necessarily more difficult, there are just more types of problems to prepare for. Today and tomorrow, we will review each type.
  6. 6. The distance between A and B is | | | | | | | | | | | | | | -5 4 A B | -5 – 4 | = | -9 | = 9 Remember: Distance is always positive
  7. 7. A B The Distance Formula Is Derived From The Pythagorean Formula 6 15 6² + 15² = C² 𝟐𝟔𝟏=C As you can see, the shortest distance between two points is... A straight line; 16.16 < 21
  8. 8. Distance Formula Dist. = ( x2 - x1 )² + ( y2 - y1 )² Remember the order ( x , y ) All answers are positive
  9. 9. Find the distance between the two points on the graph. The Distance Formula: What is the distance along the x axis? What is the distance along the y axis? Let's first use the P.T. to find the distance: a2 + b2 = c2 Now, let's use the distance formula.... =
  10. 10. Find the distance between: ( 3 – 8 )² + ( 6 - 10 )² ( -5 )² + ( -4 )² 25 + 16 41 = 6.40 ( 8 – 3 )² + ( 10 – 6 )² ( 5 )² + ( 4 )² 25 + 16 41 =6.40 ( 3 , 6 ) and ( 8 , 10 ) Find the distance between: ( 8 , 10 ) and ( 3 , 6 )
  11. 11. Find the distance between the two points (3, 𝟒) (9, −𝟒) (x1,y1) (x2, y2) 𝒅 = (𝒙 𝟐 − 𝒙 𝟏) 𝟐+(𝒚 𝟐 − 𝒚 𝟏) 𝟐 𝒅 = 𝟗 − (𝟑) 𝟐 + (−𝟒 − 𝟒) 𝟐 𝒅 = 𝟔 𝟐 + (−𝟖) 𝟐 𝒅 = 𝟏𝟎𝟎 𝒅 = 𝟏𝟎
  12. 12. Find the distance of the line. 1. (−𝟒, 1) (−𝟐, 3)(x1, y1) (x2, y2) 𝒅 = (𝒙 𝟐 − 𝒙 𝟏) 𝟐+(𝒚 𝟐 − 𝒚 𝟏) 𝟐 𝒅 = (−𝟐 − −𝟒 ) 𝟐+(𝟑 − 𝟏) 𝟐 𝒅 = 𝟐 𝟐 + (𝟐) 𝟐 𝒅 = 𝟐 𝟐 𝒅 = 𝟒 + 𝟒 𝒅 = 𝟖 𝒅 = 𝟐 ∙ 𝟒
  13. 13. Find the distance between:
  14. 14. The Distance Formula:
  15. 15. Class Work: See Handout
  16. 16. Review Graphing y x ( 0,0 ) Origin Positive Negative Order ( X,Y ) Quadrant I Quadrant II Quadrant III Quadrant IV

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