Distance Formula in Coordinate Geometry

Introduction

• The video lesson discusses the distance formula in coordinate geometry.
• The focus is on calculating the distance between two points in a coordinate plane.

Example 1: Distance from Point P to Point Q

• Points:
  • Point P: (-2, 1)
  • Point Q: (4, 3)
• Formula:
  • Distance = ( \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} )
• Substitution:
  • ( x_1 = -2, y_1 = 1, x_2 = 4, y_2 = 3 )
  • ( x_2 - x_1 = 4 - (-2) = 4 + 2 = 6 )
  • ( y_2 - y_1 = 3 - 1 = 2 )
• Calculation:
  • ( 6^2 = 36 )
  • ( 2^2 = 4 )
  • Distance = ( \sqrt{36 + 4} = \sqrt{40} )
  • Simplified: ( 2\sqrt{10} ) or approximately 6.32 units

Example 2: Distance Between Point A and Point B

• Points:
  • Point A: (1, 6)
  • Point B: (5, -2)
• Substitution:
  • ( x_1 = 1, y_1 = 6, x_2 = 5, y_2 = -2 )
  • ( x_2 - x_1 = 5 - 1 = 4 )
  • ( y_2 - y_1 = -2 - 6 = -8 )
• Calculation:
  • ( 4^2 = 16 )
  • ( (-8)^2 = 64 )
  • Distance = ( \sqrt{16 + 64} = \sqrt{80} )
  • Simplified: ( 4\sqrt{5} ) or approximately 8.94 units

Practice Questions

• Ten practice questions are provided to test understanding of the distance formula.
  • Example answers:
    • Question 1: 8 units
    • Question 2: 15 units
    • Question 3: 11.4 units
    • Question 4: 13 units
    • Question 5: 6.4 units
    • Question 6: 13 units
    • Question 7: 10.3 units
    • Question 8: 11.66 units
    • Question 9: 13.6 units
    • Question 10: 12.81 units

Conclusion

• Encouragement to share scores in the comments section.
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