DIASTANCE AND MIDPOINT
- 1. DISTANCE FORMULA APRIL JAVE MASUKAT
- 2. OBJECTIVE Lets Started • TO DEFINE AND APPLY THE DISTANCE FORMULA
- 3. Plot the following points. (1, 4) and (6,4) (2, 5) and (2, -2) (1, -2) and (4, 6)
- 4. SLOPE
- 7. PYTHAGOREAN THEOREM d =(Δ x) + (Δ y) c = a + b 2 2 2 2 2 2
- 8. BY SUBSTITUTION, d =(Δ x) + (Δ y) 2 2 2 d =(x - x ) + (y - y ) 2 2 2 2 1 2 1
- 10. Find the distance between the following points. M (1, 1/2) N (-1/2, 2/3)
- 11. Find the distance of the following points. A (0, 6) and B(5,0) C (-3, -3) and D(2, 1) E (-4, 1) and F(0, 4) I (3, 1/2) and J (2, 3/2)
- 12. MIDPOINT FORMULA
- 13. FORMULA M (x , y)= x + x , y + y 2 1 2 1 ( ) 2 2 (x , y) (x , y) (x , y) 1 2 2 1
- 14. Find the midpont between the following points. A (6, 4) B (8, 2)
- 15. A line segment AB has its midpoint at M (5, -1). Point A has coordinates (2,3). Find the coordinates of B.
- 16. Locate the midpoints of the line segments joining the given points. 1. A (-3, -4), B (2, 1) 2. C (3, -2), D (-4, 5)
- 17. 3. The midpoint of a line segment AB is at the point M (-4, -3). The point A has coordinates (8 , -5). Find the coordinates of B.
- 18. Quiz. 1 whole sheet of paper. I. Find the distance and locate the midpoints of the line segments joining the given points. (Graph) 1. A (4, 6), B (8, -12) 2. C (2, 5), D (7, -4) II. The midpoint of a line segment AB is at the point M (-7, 2). The x coordinate of A is at 5, and the y coordinate of B is at -9. Find the points A and B.
- 19. 1. A (4, 6), B (8, -12) d = 𝒙𝟐 − 𝒙𝟏 𝟐 + (𝒚𝟐 − 𝒚𝟏)𝟐 d = 𝟖 − 𝟒 𝟐 + (−𝟏𝟐 − 𝟔)𝟐 d = 𝟒 𝟐 + (−𝟏𝟖)𝟐 d = 𝟏𝟔 + 𝟑𝟐𝟒 d = 𝟑𝟒𝟎 d = 𝟐 𝟖𝟓 𝒐𝒓 𝟏𝟖. 𝟒 𝒖𝒏𝒊𝒕𝒔 distance 5 pts
- 20. 1. A (4, 6), B (8, -12) 𝑴 𝒙, 𝒚 = 𝒙𝟏 + 𝒙𝟐 𝟐 , 𝒚𝟏 + 𝒚𝟐 𝟐 𝑴 𝒙, 𝒚 = 𝟒 + 𝟖 𝟐 , 𝟔 + (−𝟏𝟐) 𝟐 𝑴 𝒙, 𝒚 = 𝟏𝟐 𝟐 , −𝟔 𝟐 𝑴 𝒙, 𝒚 = 𝟔, −𝟑 midpoint 5 pts
- 21. 5 pts
- 22. 2. C (2, 5), D (7, -4) d = 𝒙𝟐 − 𝒙𝟏 𝟐 + (𝒚𝟐 − 𝒚𝟏)𝟐 d = 𝟕 − 𝟐 𝟐 + (−𝟒 − 𝟓)𝟐 d = 𝟓 𝟐 + (−𝟗)𝟐 d = 𝟐𝟓 + 𝟖𝟏 d = 𝟏𝟎𝟔 𝒐𝒓 𝟏𝟎. 𝟑 𝒖𝒏𝒊𝒕𝒔 distance 5 pts
- 23. 2. C (2, 5), D (7, -4) 𝑴 𝒙, 𝒚 = 𝒙𝟏 + 𝒙𝟐 𝟐 , 𝒚𝟏 + 𝒚𝟐 𝟐 𝑴 𝒙, 𝒚 = 𝟐 + 𝟕 𝟐 , 𝟓 + (−𝟒) 𝟐 𝑴 𝒙, 𝒚 = 𝟗 𝟐 , 𝟏 𝟐 𝑴 𝒙, 𝒚 = 𝟒. 𝟓, 𝟎. 𝟓 midpoint 5 pts
- 24. 5 pts
- 25. The midpoint of a line segment AB is at the point M (-7, 2). The x coordinate of A is at 5, and the y coordinate of B is at - 9. Find the points A and B. M (-7, 2) A (5 , 𝒚𝟏) B (𝒙𝟐, -9) M (x , y) A (𝒙𝟏, 𝒚𝟏) B (𝒙𝟐, 𝒚𝟐)
- 26. M (-7, 2) A (5 , 𝒚𝟏) B (𝒙𝟐, -9) M (x , y) A (𝒙𝟏, 𝒚𝟏) B (𝒙𝟐, 𝒚𝟐) y = 𝒚𝟏 +𝒚 𝟐 2 = 𝒚𝟏+(−𝟗) 𝟐 (2) 2 = 𝒚𝟏+(−𝟗) 𝟐 (2) 4 = 𝒚𝟏 + (−𝟗) 4 + (+9) = 𝒚𝟏 + (−𝟗)+ 9 +13 = 𝒚𝟏 A (5 ,13) 5 pts
- 27. M (-7, 2) A (5 , 𝒚𝟏) B (𝒙𝟐, -9) M (x , y) A (𝒙𝟏, 𝒚𝟏) B (𝒙𝟐, 𝒚𝟐) x = 𝒙𝟏 + 𝒙𝟐 𝟐 -7 = 𝟓 + 𝒙𝟐 𝟐 (2) -7 = 𝟓 + 𝒙𝟐 𝟐 (2) -14 = 5 + 𝒙𝟐 -14 + (-5) = 5 + 𝒙𝟐 + (-5) -19 = 𝒙𝟐 B (-19, -9) 5 pts
- 28. 5 pts