SOLUTION: I have a chart with points (-8, -10) and (6, -4). What is the length between the two points?

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Question 296484: I have a chart with points (-8, -10) and (6, -4). What is the length between the two points?
Found 2 solutions by alicealc, Edwin McCravy:
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
the distance between 2 point can be solved by using the formula:
distance+=+sqrt%28%28x2-x1%29%5E2%2B%28y2-y1%29%5E2%29
so, if the points are (-8,-10) and (6, -4)
distance+=+sqrt%28%286-%28-8%29%29%5E2%2B%28-4-%28-10%29%29%5E2%29
distance+=+sqrt%2814%5E2%2B6%5E2%29
distance+=+sqrt%28196%2B36%29
distance+=+sqrt%28232%29
distance+=+sqrt%284%2A58%29
distance+=+2%2Asqrt%2858%29

Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
I have a chart with points (-8, -10) and (6, -4). What is the length between the two points? 

 

Now complete a right triangle with that line as its hypotenuse.  Now
there are two ways you can draw the right triangle. Either of these two
ways

  

Regardless of which way you draw the triangle, 

1. the horizontal side of that right triangle is 14 units long (count them!). 
2. the vertical side of that right triangle is 6 units long (count them!).

Therefore the Pythagorean theorem tells us that c%5E2=a%5E2%2Bb%5E2
where c is the hypotenuse, and a and b are the other two sides.  So if
we call the distance between the two points c, then we calculate:

c%5E2=a%5E2%2Bb%5E2
c%5E2=14%5E2%2B6%5E2
c%5E2=196%2B36
c%5E2=232
c=sqrt%28232%29
c=sqrt%284%2A58%29
c=sqrt%284%29%2Asqrt%2858%29
c=2%2Asqrt%2858%29

or approximately 15.23154621

Edwin