SOLUTION: AB are the diameter of a circle. If A=(2,-6) and B=(4,2), write down the coordinates of the centre of the circle

Algebra ->  Coordinate-system -> SOLUTION: AB are the diameter of a circle. If A=(2,-6) and B=(4,2), write down the coordinates of the centre of the circle      Log On


   

Question 836275: AB are the diameter of a circle. If A=(2,-6) and B=(4,2), write down the coordinates of the centre of the circle
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Find the midpoint of AB

Solved by pluggable solver: Midpoint


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (2, -6), we can say (x1, y1) = (2, -6)
So x%5B1%5D+=+2, y%5B1%5D+=+-6


Since the second point is (4, 2), we can also say (x2, y2) = (4, 2)
So x%5B2%5D+=+4, y%5B2%5D+=+2


Put this all together to get: x%5B1%5D+=+2, y%5B1%5D+=+-6, x%5B2%5D+=+4, and y%5B2%5D+=+2

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Finding the x coordinate of the midpoint: Add up the corresponding x coordinates x1 and x2 and divide that sum by 2


X Coordinate of Midpoint = %28x%5B1%5D%2Bx%5B2%5D%29%2F2


X Coordinate of Midpoint = %282%2B4%29%2F2


X Coordinate of Midpoint = 6%2F2


X Coordinate of Midpoint = 3



So the x coordinate of the midpoint is 3


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Finding the y coordinate of the midpoint: Add up the corresponding y coordinates y1 and y2 and divide that sum by 2


Y Coordinate of Midpoint = %28y%5B1%5D%2By%5B2%5D%29%2F2


Y Coordinate of Midpoint = %28-6%2B2%29%2F2


Y Coordinate of Midpoint = -4%2F2


Y Coordinate of Midpoint = -2


So the y coordinate of the midpoint is -2



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Summary:


The midpoint of the segment joining the two points (2, -6) and (4, 2) is (3, -2).


So the answer is (3, -2)





So the center of the circle is (3,-2)