SOLUTION: Find the distance between the following points. (8,5) and (0,20)

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Question 647495: Find the distance between the following points.
(8,5) and (0,20)
Found 2 solutions by jim_thompson5910, swincher4391:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Note: is the first point . So this means that x%5B1%5D=8 and y%5B1%5D=5.
Also, is the second point . So this means that x%5B2%5D=0 and y%5B2%5D=20.


d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 Start with the distance formula.


d=sqrt%28%288-0%29%5E2%2B%285-20%29%5E2%29 Plug in x%5B1%5D=8, x%5B2%5D=0, y%5B1%5D=5, and y%5B2%5D=20.


d=sqrt%28%288%29%5E2%2B%285-20%29%5E2%29 Subtract 0 from 8 to get 8.


d=sqrt%28%288%29%5E2%2B%28-15%29%5E2%29 Subtract 20 from 5 to get -15.


d=sqrt%2864%2B%28-15%29%5E2%29 Square 8 to get 64.


d=sqrt%2864%2B225%29 Square -15 to get 225.


d=sqrt%28289%29 Add 64 to 225 to get 289.


d=17 Take the square root of 289 to get 17.


So our answer is d=17


So the distance between the two points is 17 units.

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Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for distance is simply (maybe not simply)
Where (x1,y1) and (x2,y2) are just two points.
sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29
------
If you understand the distance formula you can skip this.
This formula is NOT random.
This formula pieces together slope and the Pythagorean Theorem.
Recall that for slope m = (change in y)/(change in x) = (y2-y1)/(x2-x1).
Now, visualize the distance from y1 to y2 and x1 to x2 as sides of a right triangle. x1 to x2 would be side a and y1 to y2 would be side b. The distance would be our hypotenuse, c. Let d be distance. So (c=d).
a^2 + b^2 = c^2
(x2-x1)^2 + (y2-y1)^2 = c^2
sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29+=+c
sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29+=+d
Now onto your problem.
------------------------
(8,5) and (0,20) are our points.
x1 = 8
y1 = 5
x2 = 0
y2 = 20
sqrt%28%280-8%29%5E2+%2B+%2820-5%29%5E2%29
sqrt%28%28-8%29%5E2+%2B+15%5E2%29
sqrt%2864+%2B+225%29
sqrt%28289%29
d+=+17