Question 1190993
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The x coordinates of points A and B are 2 and -3 respectively.
Add up the x values: 2 + (-3) = -1
Then cut that result in half: -1/2 = -0.5
The x coordinate of the midpoint is x = -0.5


Repeat for the y coordinate of the midpoint.
Add: -2+3 = 1
Cut in half: 1/2 = 0.5
The y coordinate of the midpoint is y = 0.5


The midpoint of segment AB is (-0.5, 0.5)
This means (h,k) = (-0.5, 0.5) is the center of the circle, since AB is a diameter.
In fraction form that would be (h,k) = (-1/2, 1/2)
Let's label this point C. 


To get the radius, find the distance from A to C.
We'll use the aptly named distance formula.


A = (x1,y1) = (2,-2) and C = (x2, y2) = (-0.5, 0.5)


*[tex \large d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}]


*[tex \large d = \sqrt{(2-(-0.5))^2 + (-2-0.5)^2}]


*[tex \large d = \sqrt{(2+0.5)^2 + (-2-0.5)^2}]


*[tex \large d = \sqrt{(2.5)^2 + (-2.5)^2}]


*[tex \large d = \sqrt{6.25 + 6.25}]


*[tex \large d = \sqrt{12.5}]
The exact length of segment AC is *[tex \large \sqrt{12.5}]


This means the radius is *[tex \large r = \sqrt{12.5}]
Squaring both sides gets us *[tex \large r^2 = 12.5]


So we have
*[tex \large (x-h)^2 + (y-k)^2 = r^2]


*[tex \large (x-(-0.5))^2 + (y-0.5)^2 = 12.5]


*[tex \large (x+0.5)^2 + (y-0.5)^2 = 12.5]
which is the equation of the circle.


Optionally you can replace each 0.5 with 1/2, and you can replace 12.5 with the improper fraction 25/2
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