SOLUTION: Find the distance between the points (-3, 2) and (-5, 6).

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Question 113322: Find the distance between the points (-3, 2) and (-5, 6).
Found 2 solutions by checkley71, solver91311:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
FIRST WE FIND THE X & Y DISTANCE:
-3+5=2 FOR THE X DISTANCE.
6-2=4 FOR THE Y DISTANCE.
NOW WE HAVE A RIGHT TRIANGLE WITH SIDES OF 2 & 4.
NOW USING THE PYTHAGOREAN FORMULA WE FIND THE HYPOTENUSE (DISTANCE BETWEEN THESE 2 POINTS)
2^2+4^2=H^2
4+16=H^2
20=H^2
H=SQRT20
H=4.47 ANSWER FOR THE DISTANCE BETWEEN THESE 2 POINTS.
PROOF
2^2+4^2=4.47^2
4+16=20
20=20

Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!
drawing%28600%2C600%2C-8%2C2%2C-2%2C8%2C%0D%0A+++grid%281%29%2C%0D%0A+++locate%28-3.2%2C1.7%2CA%28-3%2C2%29%29%2C%0D%0A+++locate%28-4.8%2C6.5%2CB%28-5%2C6%29%29%2C%0D%0A+++locate%28-4.8%2C1.7%2CC%28-5%2C2%29%29%2C%0D%0A+++red%28circle%28-3%2C2%2C.1%29%29%2C%0D%0A+++red%28circle%28-5%2C6%2C.1%29%29%2C%0D%0A+++blue%28circle%28-5%2C2%2C.1%29%29%2C%0D%0A+++green%28line%28-3%2C2%2C-5%2C6%29%29%2C%0D%0A+++line%28-3%2C2%2C-5%2C2%29%2C%0D%0A+++line%28-5%2C6%2C-5%2C2%29%0D%0A%29

To determine the distance between two points in a plane, use the distance formula. I included the diagram so that you can see why the distance formula works.

The distance formula is d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29. This is just an application of the Pythagorean Theorem because the length of AC in the diagram is abs%28x%5B1%5D-x%5B2%5D%29 and the length of BC is abs%28y%5B1%5D-y%5B2%5D%29.

For your problem, just plug in the values:

d=sqrt%28%28-3-%28-5%29%29%5E2%2B%282-6%29%5E2%29

Now all we have to do is the arithmetic:
d=sqrt%28%282%29%5E2%2B%28-4%29%5E2%29
d=sqrt%284%2B16%29
d=sqrt%2820%29
d=sqrt%284%2A5%29
d=2%2Asqrt%285%29

Hope that helps,
John