Question
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  1. ; Distance Formula

Ask by Riley Barrett. in the United States
Jan 23,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The distances between the points are as follows:
  • to : units (approximately 11.18 units)
  • to : units (approximately 13.04 units)
  • to : units (approximately 6.71 units)
  • to : units (approximately 6.71 units)
  • to : units (approximately 13.04 units)
  • to : units (approximately 11.18 units)

Solution

Sure! Let’s calculate the distances between each pair of points , , , and using the Distance Formula.

Distance Formula

The distance between two points and is given by:

Calculations

We’ll calculate the distance for each pair:
  1. Distance between and :
  2. Distance between and :
  3. Distance between and :
  4. Distance between and :
  5. Distance between and :
  6. Distance between and :

Summary of Distances

Pair Distance (Exact Form) Approximate Distance
N & O 11.18 units
N & P 13.04 units
N & Q 6.71 units
O & P 6.71 units
O & Q 13.04 units
P & Q 11.18 units

Visualization

To better understand the distances, you can plot the points on a coordinate plane:
  • N(-4, 5)
  • O(6, 0)
  • P(3, -6)
  • Q(-7, -1)
Connecting each pair of points will help visualize the distances calculated above.

Conclusion

Using the Distance Formula, we’ve calculated all pairwise distances between the points , , , and . This method is fundamental in coordinate geometry for determining the length between any two points in a plane.

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The Deep Dive

To calculate the distance between two points, you can use the Distance Formula, which is given by . For example, the distance between points N and O is calculated as .
Additionally, when using the Distance Formula, a common mistake is forgetting to square the differences! For instance, it’s crucial to ensure that both subtractions are correctly set up; if you mistakenly calculate one of them as without squaring, you may end up with the wrong distance. Double-check your arithmetic to avoid such errors and ensure precise results.

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