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Question 1039212: I have another questuon pls.
The diameter of a cirlce whose endpoints are (-3,-3) and (3,3)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if the end points of the diameter are (-3,-3) and (3,3), then the length of the diameter would be the length of the line segment between those 2 points.
you have:
(x1,y1) = (-3,-3)
(x2,y2) = (3,3)
let d represent length of the diameter.
d = sqrt((x2-x1)^2 + (y2-y1)^2).
formula becomes d = sqrt((3 - (-3))^2 + (3 - (-3))^2).
simplify this to get d = sqrt(3+3)^2 + (3+3)^2).
simplify further to get d = sqrt(6^2 + 6^2).
simplify further to get d = sqrt(36 + 36).
simplify further to get d = sqrt(72).
simplify further to get d = 6*sqrt(2).
the solution to your problem is that that the length of the diameter of the circle is 6 * sqrt(2).
if that's all you wanted, you can stop here.
the rest is just more stuff if you want to learn more about this problem.
the general formula of a circle is (x-h)^2 + (y-k)^2 = r^2
(h,k) is the center of the circle.
r is the radius.
we got d = 6*sqrt(2).
that's the length of the diameter.
the length of the radius is half that, so the length of the radius would be 3*sqrt(2).
that would be r.
r^2 would be (3*sqrt(2))^2 = 9*2 = 18.
the center of your circle is at the midpoint of the line segment between (-3,-3) and (3,3).
the formula for midpoint is ((x1+x2)/2,(y1+y2)/2).
that puts your midpoint at (0,0) which is the center of the circle.
the formula for your circle becomes x^2 + y^2 = 18.
that is shown in the following graph with the points of (-3,-3) and (3,3) displayed because they lie on the line of the equation of y = x.
how i derive that is based on the slope intercept form of the equation for a straight line that is y = mx + b, where m is the slope and b is the y-intercept.
the slope is (y2-y1)/(x2-x1) which becomes 6/6 which becomes 1.
the y-intercerpt is found by taking any one of the points and replacing x and y with them in the general equation and then solving for b.
y = mx + b becomes y = x + b which becomes 3 = 3 + b if we use the point (3,3).
solve for b to get b = 0.
the slope intercept form of the equation through the points (-3,-3) and (3,3) is y = x.
here's the graph.
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