SOLUTION: Find the distance between these two points: (6,4) and (-3,5)

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Question 179715: Find the distance between these two points:
(6,4) and (-3,5)

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Find the distance between these two points:
(6,4) and (-3,5)

There are two ways to do this:

Plot the points and connect them with a line segment:

drawing%28400%2C291.1%2C-4%2C7%2C-1%2C7%2C+grid%281%29%2C+line%286%2C4%2C-3%2C5%29+%29

Then we draw in these two line segments forming a right
triangle:



We count how many units long the bottom (horizontal) side of 
that right triangle is and see that it is 9 units long. Then 
we see that the left (vertical) side of the right triangle 
is only 1 unit long. And the hypotenuse is the distance
between the desired points.  






So we use the Pythagorean 
theorem 

c%5E2=a%5E2%2Bb%5E2
c%5E2=9%5E2%2B1%5E2
c%5E2=81%2B1
c%5E2=82
sqrt%28c%5E2%29=sqrt%2882%29
c=sqrt%2882%29

Another way is to memorize the formula

d=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29

and plug in x%5B1%5D=6, x%5B2%5D=-3, y%5B1%5D=4, y%5B2%5D=5

d=sqrt%28%28%28-3%29-%286%29%29%5E2%2B%28%285%29-%284%29%29%5E2+%29

d=sqrt%28%28-9%29%5E2%2B%281%29%5E2%29%29++

d=sqrt%2881%2B1%29

d=sqrt%2882%29

Either way we get the same answer.

The distance is sqrt%2882%29

Edwin