Distance between two points
Here is how to calculate the distance between two points when you know their coordinates:
Let us call the two points A and B
We can run lines down from A, and along from B, to make a Right Angled Triangle.
And with a little help from Pythagoras we know that: a2 + b2 = c2
Now label the coordinates of points A and B.
xA means the x-coordinate of point A yA means the y-coordinate of point A
The horizontal distance a is (xA − xB)
The vertical distance b is (yA − yB)
Now we can solve for c (the distance between the points):
Start with: c2 = a2 + b2
Put in the calculations for a and b: c2 = (xA − xB)2 + (yA − yB)2
And the final result: c = square root of [(xA-xB)^2+(yA-yB)^2]
Examples
Proportional division of a line (section formula)
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