The midpoint of the diameter endpoints is the center of the circle...
((2+9)/2, (4+4)/2)
(5.5, 4) is the center of the circle...
The distance between the two endpoints is the diameter of the circle...
d^2=(4-4)^2+(9-2)^2
d^2=0+49
d^2=49
d=7
So the radius is d/2 which is 3.5
Now the equation of a circle is:
(x-h)^2+(y-k)^2=r^2 where (h,k) is the coordinates of the center and r is the radius.
Earlier we found (h,k) to be (5.5, 4) and r=3.5 so our equation is:
(x-5.5)^2+(y-4)^2=3.5^2
(x-5.5)^2+(y-4)^2=12.25
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Let H = Henry
Let R = Roger
Let S = Sandy
H = 3R -> H = 3y
S = 9 + H -> S = 9 + 3y
R = y
Sandy has 3y + 9 CDs more than Roger.
The midpoint of a line segment is the average of the endpoint's coordinates, mathematically:
mp=((x1+x2)/2, (y1+y2)/2)
In this case:
(-4,6)=((8+x)/2, (-2+y)/2)
(-8,12)=((8+x),(y-2))
(-16, 14)=(x,y)