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!
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!
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 \displaystyle (\frac {x_{1}+x_{2}}{2} , \frac {y_{1}+y_{2}}{2}) $
Sub in the values to find the midpoint
Now you know the centre,you can find the radius: $\displaystyle r = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ but in this case $\displaystyle (x_1,y_1)$ is the centre and $\displaystyle (x_2,y_2)$ is either point.
Once you know the radius use the equation of a circle to pick any old points: $\displaystyle (x-a)^2 + (y-b)^2 = r^2$ with centre (a,b) and radius r
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)
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
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Do you know the formula for distance between two points?
The distance from $\displaystyle (x_1, y_1)$ to $\displaystyle (x_2, y_2)$ is $\displaystyle \sqrt{(x_1- x_2)^2+ (y_1-y_2)^2}$.
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.)