Math project

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Math project

  1. 1. MATH SOLUTIONS By: Kasi, Jessica, Bhagy, and Janie!
  2. 2. QUESTION: ? A triangle has vertices A (-4,0), B (2,6) and C (8, -4).Determine the exact coordinates of the circumcentre
  3. 3. STEPS TO SOLUTION:• 1) FIND MIDPOINT 2) FIND SLOPE• 3) NEGATIVE RECIPROCAL 4) EQUATION OF PERPENDICULAR BISECTOR• 5) REPEAT.
  4. 4. PERPENDICULARExplanation:BISECTOR for each side.
  5. 5. So how do we do it?y=m(x-p)+q
  6. 6. Perpendicular Bisector of AB 1) Find the midpoint of AB! Coordinate points: A (-4,0) B (2,6) C (8, -4)MIDPOINT M = (-4+2), (0+6) : 2 2
  7. 7. Perpendicular Bisector of AB 2) Find the slope of AB m = 6-0 m = 6 m =1 2-(-4) 6 3) Opposite Reciprocal = -1
  8. 8. Equation of Perpendicular Bisector for AB y = m(x-p)+q y = -1 (x+1) + 3 y = -x-1+3 y = -x + 2
  9. 9. Perpendicular Bisector of BCLet’s refresh the steps:To find the perpendicular bisector foreach side • 1)Midpoint • 2)Slope • 3)Opposite Reciprocal • 4) Equation of Perpendicular Bisector
  10. 10. Perpendicular Bisector of BC Coordinate points: A (-4,0) B (2,6) C (8, -4)Midpoint: Slope: Negative Reciprocal: M = (2+8), (6+(-4) m = -4 - 6 = 3 8-2 5 2 2 = -10 = 10 , 2 6 2 2 = -5 = ( 5, 1) 3
  11. 11. Equation of y=m(x-p)+qy=m(x-p)+q Perpendicular Bisector for BC y = 3 (x-5)+1 y = 3x - 3 +1 5 5 y = 3x -15/5 +1 y = 3x -2 5 5
  12. 12. Perpendicular Bisector of1) Slope: CA 3) Negative Reciprocal M = ( 8 + ( -4) , (-4 - 0) m = 3 2 2M = 4 , -4 2 2 4) Equation of Perpendicular Bisector for CAM = ( 2 , -2 )2) Midpoint: y=3(x-2)-2 y = 3x - 6 -2m = 0 - ( - 4) m= 4 m = 1 -12 -3 y = 3x - 8 -4-8
  13. 13. Three Equations AB y = -x + 2 y = 3x -2 BC 5 CA y = 3x - 8
  14. 14. Intersection Points (Circumcentre) (Circumcentre) * Using Substitution * AB & BC -x + 2 = 3x - 2y = -x + 2 5y = 3x -2 2 + 2 = 3x + 1x x 5 5 1 x5 5 4 = 3x + 5x AB 5 5y = -x + 2 4 = 8x 5y = -2.5 + 2 4 = 1.6xy = -0.5 1.6 1.6 2.5 = x
  15. 15. Let’s check/verify! Verify: x y (2.5 , - 0.5) CA y = 3x - 8 - 0.5 = 3 (2.5) - 8 - 0.5 = 7.5 - 8 - 0. 5 = - 0.5
  16. 16. Le t’s g rap h it!
  17. 17. THE END : )

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