SOLUTION: A rectangle has its vertices at (3,1), (3,2),(5,2)and (5,1). What is the length of its diagonal?

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Question 172923: A rectangle has its vertices at (3,1), (3,2),(5,2)and (5,1). What is the length of its diagonal?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you draw out the rectangle, you'll see that one diagonal runs from (3,1) to (5,2)


So let's find the distance from (3,1) to (5,2)


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%283-5%29%5E2%2B%281-2%29%5E2%29 Plug in x%5B1%5D=3, x%5B2%5D=5, y%5B1%5D=1, and y%5B2%5D=2.


d=sqrt%28%28-2%29%5E2%2B%281-2%29%5E2%29 Subtract 5 from 3 to get -2.


d=sqrt%28%28-2%29%5E2%2B%28-1%29%5E2%29 Subtract 2 from 1 to get -1.


d=sqrt%284%2B%28-1%29%5E2%29 Square -2 to get 4.


d=sqrt%284%2B1%29 Square -1 to get 1.


d=sqrt%285%29 Add 4 to 1 to get 5.


So our answer is d=sqrt%285%29


Which approximates to d=2.236




So the distance between the two points is approximately 2.236 units.


This means that the length of the diagonal is approximately 2.236 units