Using the Distance Formula

In this lecture, we practiced using the distance formula to find the distance between two points when only the points, not the lines, are given.

Key Concepts

• Distance Formula: It is often misunderstood. It's essentially applying Pythagoras’ theorem but in a formulaic way: [ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} ]
• The formula requires substituting the coordinates of two points (A and B for example) to find the distance between them.

Solving Problems with the Distance Formula

Problem 1: Finding Distance of AB

• Procedure:
  • Choose one point as Point 2 (A or B), it doesn’t matter which one.
  • Identify the x and y values of Point 2 and Point 1.
  • Substitute these values into the distance formula.
  • Use a calculator to compute the distance ensuring to consider all signs correctly.
  • Example provided: Points given were (-2, 4) and (-1, 9)
  • Calculation resulted in a distance of √26, which rounds to 5.10 to two decimal places.

Problem 2: Finding Length of CD

• Procedure:
  • Again, choose one point as Point 2.
  • Identify the x and y values of the respective points.
  • Fill these into the formula similarly as before.
  • Example provided: Points given were (-3, 4) and (2, 7)
  • Calculation resulted in a distance of 5.83 to two decimal places.

Tips

• The order in which you choose your points (Point 1 and Point 2) doesn’t affect the result.
• The calculator handles the computation of squares and square roots, so ensure entries are correct.
• Rounding is crucial in problems where results need to be expressed to specific decimal places.

Conclusion

• By following these steps, one should become comfortable with using the distance formula to find distances between points. The lecture emphasizes practicing this method to gain confidence.