Points on a circle.

**dt1500** · December 14th 2010, 02:36 PM

Guys, i have one question in math.
here it it.
The diameter of a circle has the endpoints (9,5) and (3,-8). Find the center of the circle and at least two other points on the circle.
thank you!

**jgv115** · December 14th 2010, 02:52 PM

Well since we know the diameter's endpoints the centre of the circle must be the midpoint of the 2 points.

We can use the midpoint formula:

$\displaystyle (\frac {x_{1}+x_{2}}{2} , \frac {y_{1}+y_{2}}{2})$

Sub in the values to find the midpoint

**dt1500** · December 14th 2010, 02:56 PM

yes. i did that and found the midpoint of (6,-1.5)
but doesn't it says that i have to find other two points on the circle?
i'm so confused.

**e^(i*pi)** · December 14th 2010, 03:41 PM

Now you know the centre,you can find the radius: $r = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ but in this case $(x_1,y_1)$ is the centre and $(x_2,y_2)$ is either point.

Once you know the radius use the equation of a circle to pick any old points: $(x-a)^2 + (y-b)^2 = r^2$ with centre (a,b) and radius r

**dt1500** · December 14th 2010, 03:56 PM

my teacher didn't taught us anything about the square rot and that big "E" thing.

**jgv115** · December 14th 2010, 04:02 PM

lol the big E thing is his sig, it has nothing to do with his post

HAHAHAHAHAH xD

**pickslides** · December 14th 2010, 04:06 PM

The big E thing is in the poster's signature, it is not part of the response!

You have been shown how to find the centre in post #2 and from this apply the radius from post #4 to this centre point, here's two easy solutions, given (x,y) is the centre and r your radius then you have (x+r,y) and (x,y+r)

**bjhopper** · December 15th 2010, 06:16 AM

the slope diagramof the given diameter points is 13/6. Its radius slope diagram is 6.5/3.
A diameter perpendicular to the given diameter has a slope of -6/13 and its radius slope diagram is -3/6.5.
Working with these new radius slopes and starting at the circle center the end points on the circle are determined to be (-.5,1.5) and (12.5,-4.5) by moving 6.5 points right and left of center and 3 points up and down of center

bjh

**HallsofIvy** · December 15th 2010, 08:09 AM

Do you know the formula for distance between two points?

The distance from $(x_1, y_1)$ to $(x_2, y_2)$ is $\sqrt{(x_1- x_2)^2+ (y_1-y_2)^2}$ .

You can use that to find the distance form (6, 1.5), the center of the circle, to either (9, 5) or (3, -8), the radius of the circle, then find values of (x, y) such that the distance from (x, y) to (6, -1.5) is that radius. (There will be an infinite number of such points, of course. Choose some convenient value for x and determine y satifying that equation.)

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