_{1 }+ X

_{2}) / 2

_{1}+ Y

_{2}) / 2

Please help me.

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Denise W. | Elementary / Middle / High School Math TutorElementary / Middle / High School Math T...

The center of the circle is going to be at the half-way point of the diameter (or equal to the radius of the circle).

If you draw yourself a quick sketch of the two points you will see that the center point is equal to half the horizontal distance between the two points and half the vertical distance between the two points.

To work out these differences, add up the horizontal co-ordinates and half them (X_{1
}+ X_{2}) / 2

and do the same to the vertical co-ordinates (Y_{1} + Y_{2}) / 2

This will leave you with the co-ordinates of the center point of the circle.

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

Coordinate of a mid point of a line segment with end point coordinates of

X_{m = ( }X_{1 +}X_{2)/ 2 ,}

The center of a circle is midway between end points of Diameter, Therefore:

X_{c = ( -4 +1 ) /2 =-3/2 }Y_{c = ( 3 + 6) /2=9/2}

C : ( - 3/2, 9/2)

On a coordinate plane you could see that the diameter of your circle is also the hypotenuse of a right triangle with endpoints at

point 1 (-4,3) and point 2 (1,6) the lengths of the legs of that triangle are simply (x2 - x1) and (y2 - y1)

x2 - x1 = 1--4 = 5 is the length of the one side of that triangle, the width.

y2 - y1 = 6- 3 = 3 is the length of the other side of that triangle, the height.

since you want to find the midpoint of that diameter, which is your center, (x_{c}, y_{c})

cut those lengths in half: x length is 5/2 = 2.5 and y height is 3/2 = 1.5

add those values to the first point to arrive at the center (or you can subtract them from the 2nd point)

so using (-4,3) you get -4+2.5 = -1.5 x_{c} = -1.5

and 3 + 1.5 = 4.5 so y_{c} = 4.5

so, your answer is **(-1.5,4.5) **

(additionally, to find the length of the diameter (hypotenuse) you use pythagoreans theorem, let D = c, where c^{2} = a^{2} + b^{2} and a and b are the original lengths we found above. so, D = sqrt(5^{2} + 3^{2}) = sqrt(34) = ~5.83 now you can use that to find the area and circumference of your circle! woohoo!)

The center of the circle is at the center of its diameter. Therefore, you need to find the center of the line connecting points (-4,3) and (1,6). The center of the line connecting points (x_{1},y_{1}) and (x_{2}, y_{2}) has coordinates (½*(x_{1}+x_{2});½*(y_{1}+y_{2})). If you plug in the coordinates of the points given to you, you will end up with:

C=(½(-4+1);½(3+6))=(-3/2;9/2)

So, the center of the circle is at the **point (-3/2;9/2)**

So true!

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