Question
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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:
-
Distance between
and : -
Distance between
and : -
Distance between
and : -
Distance between
and : -
Distance between
and : -
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.