SOLUTION: Find the distance between points at (4,-1) and (-2,-5). Thank you so much for all of your help!!!!!! God Bless!!!!!!

Algebra ->  Sequences-and-series -> SOLUTION: Find the distance between points at (4,-1) and (-2,-5). Thank you so much for all of your help!!!!!! God Bless!!!!!!      Log On


   



Question 391969: Find the distance between points at (4,-1) and (-2,-5).
Thank you so much for all of your help!!!!!!
God Bless!!!!!!

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


There are two ways:

First draw the two points and draw a line segment from one to the
other:



Draw a right triangle whose hypotenuse is the green line:



Count the units in the lower red leg of the right triangle and you'll find it
is 6 units long.

Count the units in the right red leg of the right triangle and you'll find it 
is 4 units long.

Use the Pythagorean theorem and find the length of the green hypotenuse:

c%5E2=a%5E2%2Bb%5E2
c%5E2=6%5E2%2B4%5E2
c%5E2=36%2B16
c%5E2=52
c=sqrt%2852%29
c=sqrt%284%2A13%29
c=2sqrt%2813%29

(4,-1) and (-2,-5).

Another way is to use the formula, which amounts to the same thing:

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

d=sqrt%28%28%28-2%29-%284%29%29%5E2%2B%28%28-5%29-%28-1%29%29%5E2%29

d=sqrt%28%28-2-4%29%5E2%2B%28-5%2B1%29%5E2%29

d=sqrt%28%28-6%29%5E2%2B%28-4%29%5E2%29

d=sqrt%2836%2B16%29

d=sqrt%2852%29

d=sqrt%284%2A13%29

d=2sqrt%2813%29

Edwin