Midpoint Between Two Points

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How to find the Midpoint between two (x,y) coordinates.

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Midpoint Between Two Points

  1. 1. Midpoint Between Points Image Source: http://facebook.com
  2. 2. The 90 mile straight section of highway lies between the towns of Balladonia and Caiguna in the Australian Outback. Some friends of ours recently drove this stretch of the Eyre Highway. If their car started making some strange noises along this section of road, would they be better off heading back to Balladonia, or continuing onto Caiguna? Well assuming there is a mechanic in each town, it would depend on whether or not they had crossed the halfway point (or "Midpoint") of their journey. Midpoint Between Points
  3. 3. 90 We need to find the Midpoint between Balladonia at (0,2) and Calguna at (90,2). Eg. We need to halve 90, and we get 45 miles OR We can add the x-coords and halve, eg. (0+90)/2 = 45 miles B C Midpoint Between Points 0
  4. 4. 5 -5 We need to find the Midpoint between Point A at (-2,-2) and Point B at (2,6) We measure Across, and we measure Up, and work out the halfway point is at x = 0, y = 2 or (0,2) A B Across = 4 squares Midpoint is 2 squares across at x = 0 Up = 8 Squares Midpoint is 4 squares up at y = 2 Midpoint Between Points
  5. 5. 5 -5 A (3, -2) B (-3,4) -3 Midpoint of Points Example We need to find the Midpoint between Point A at (3,-2) and Point B at (-3,4) Measure Across & Halve, and measure Up & Halve, and thereby work out the halfway point is at the pt x = __, y = __ or (__,__)
  6. 6. 5 -5 A (3, -2) B (-3,4) Midpoint of Points Example We need to find the Midpoint between Point A at (3,-2) and Point B at (-3,4) Measure Across & Halve, and measure Up & Halve, and thereby work out the halfway point is at the pt x = 0, y = 1 or (0,1) Across = 6 squares Midpoint is 3 squares across at x = 0 Up = 6 Squares Midpoint is 3 squares up at y = 1
  7. 7. 5 -5 To find the Midpoint between two points: Point A and Point B The midpoint is (x,y) where : x = (x1 + x2 ) / 2 and y = (y1 + y2 ) / 2 A Midpoint Formula B (x2,y2) A (x1,y1) M (x,y)
  8. 8. 5 -5 A (-2,-2) •Label the Points as A and B •Label A (x1,y1) and B (x2,y2) •Substitute the Values of (x1,y1) and (x2,y2) numbers into the Midpoint Formula: (X1+X2) / 2 and (Y1+Y2) / 2 •Calculate and write as (x,y) Midpoint Formula STEPS B (2,6) A (x1,y1) B (x2,y2)
  9. 9. 5 -5 A (-2,-2) • Substitute the Values of (x1,y1) and (x2,y2) numbers into the Midpoint Formula: (X1+X2) / 2 and (Y1+Y2) / 2 =(__+__) / 2 and (__+__) / 2 = ____ and _____ = ( ___ , ___) Midpoint Formula Example 1 B (2,6) A (x1,y1) B (x2,y2)
  10. 10. 5 -5 A (-2,-2) • Substitute the Values of (x1,y1) and (x2,y2) numbers into the Midpoint Formula: (X1+X2) / 2 and (Y1+Y2) / 2 =(-2+2) / 2 and (-2+6) / 2 = 0 and 2 = (0 , 2) Midpoint Formula Example 1 B (2,6) A (x1,y1) B (x2,y2) M (0,2)
  11. 11. 5 -5 A (-2,-2) Add the Points and Divide the Answer by two. (-2 , -2) + ( 2 , 6) ( 0 , 4) = (0 , 2) Example 1 Alternative Method B (2,6) M (0,2) Divide by 2 Add
  12. 12. 5 -5 A (__,__) B (__,__) -3 Midpoint Formula Example 2 • Substitute the Values of (x1,y1) and (x2,y2) numbers into the Midpoint Formula: (X1+X2) / 2 and (Y1+Y2) / 2 =(__+__) / 2 and (__+__) / 2 = ____ and _____ = ( ___ , ___)
  13. 13. 5 -5 A (3,-2) B (-4,4) -3 Midpoint Formula Example 2 • Substitute the Values of (x1,y1) and (x2,y2) numbers into the Midpoint Formula: (X1+X2) / 2 and (Y1+Y2) / 2 =(3+-4) / 2 and (-2+4) / 2 = -0.5 and 1 = ( -0.5 , 1) A (x1,y1) B (x2,y2) M (-0.5, 1)
  14. 14. 5 -5 A (3,-2) B (-4,4) -3 Example 2 Alternative Method M (-0.5, 1) Add the Points and Divide the Answer by two. ( 3 , -2) + (-4 , 4) (-1 , 2) = (-0.5 , 1) Divide by 2 Add
  15. 15. Blank X-Y Grid -3 3 5 -5
  16. 16. http://passyworldofmathematics.com/

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