SOLUTION: Let P(-3,6) and Q(10,1) be two points in the coordinate plane Find an equation of the circle that contains P and Q and whose center is the midpoint of the segment PQ

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Question 730942: Let P(-3,6) and Q(10,1) be two points in the coordinate plane
Find an equation of the circle that contains P and Q and whose center is the midpoint of the segment PQ
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
The standard equation of a circle with center C(,) and radius is as follows:

so, we need to find ,, and
since the circle that contains P and Q , the distance between them is equal to diameter of the circle:
Solved by pluggable solver: Distance Formula


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


Since the first point is (-3, 6), we can say (x1, y1) = (-3, 6)
So ,


Since the second point is (10, 1), we can also say (x2, y2) = (10, 1)
So ,


Put this all together to get: , , , and

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Now use the distance formula to find the distance between the two points (-3, 6) and (10, 1)






Plug in , , , and













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Answer:


The distance between the two points (-3, 6) and (10, 1) is exactly units


The approximate distance between the two points is about 13.9283882771841 units



So again,


Exact Distance: units


Approximate Distance: units




so, diameter ...=>......=>...
now find midpoint:
Solved by pluggable solver: Midpoint


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


Since the first point is (-3, 6), we can say (x1, y1) = (-3, 6)
So ,


Since the second point is (10, 1), we can also say (x2, y2) = (10, 1)
So ,


Put this all together to get: , , , and

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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 =


X Coordinate of Midpoint =


X Coordinate of Midpoint =


X Coordinate of Midpoint =



So the x coordinate of the midpoint is 3.5


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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 =


Y Coordinate of Midpoint =


Y Coordinate of Midpoint =


Y Coordinate of Midpoint =


So the y coordinate of the midpoint is 3.5



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Summary:


The midpoint of the segment joining the two points (-3, 6) and (10, 1) is (3.5, 3.5).


So the answer is (3.5, 3.5)




center is (, )=(,)...so and
...plug in ,, and
your equation is:




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