SOLUTION: a circle with center of (4,8) passes through the point (5,9) what is the area of the circle rounded to the nearest tenth of a square unit

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Question 289664: a circle with center of (4,8) passes through the point (5,9) what is the area of the circle rounded to the nearest tenth of a square unit
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Recall that the radius is the distance from the center of the circle to the edge of the circle. So to find the radius, just find the distance from (4,8) to (5,9).


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%284-5%29%5E2%2B%288-9%29%5E2%29 Plug in x%5B1%5D=4, x%5B2%5D=5, y%5B1%5D=8, and y%5B2%5D=9.


d=sqrt%28%28-1%29%5E2%2B%288-9%29%5E2%29 Subtract 5 from 4 to get -1.


d=sqrt%28%28-1%29%5E2%2B%28-1%29%5E2%29 Subtract 9 from 8 to get -1.


d=sqrt%281%2B%28-1%29%5E2%29 Square -1 to get 1.


d=sqrt%281%2B1%29 Square -1 to get 1.


d=sqrt%282%29 Add 1 to 1 to get 2.


Since d=sqrt%282%29, this means that r=sqrt%282%29 because the radius is the distance from the center to the edge of the circle.


A=pi%2Ar%5E2 Move onto the area of a circle formula


A=pi%2A%28sqrt%282%29%29%5E2 Plug in r=sqrt%282%29


A=pi%2A2 Square sqrt%282%29 to get 2.


A=2pi Rearrange the terms.


So the exact area is A=2pi which approximates to . Round this to the nearest tenth to get


So the area is approximately 6.3 square units.