The points (4, –5) and (– 4, 1) are endpoints of a diameter of a circle.
Find the center of the circle.
The mid-point Pm between two points P1(x1,y1) and P2(x2,y2) can be found by taking the mean of the x- and y-coordinates.
Thus
xm=(x1+x2)/2 and
ym=(y1+y2)/2
and the mid-point (centre of the diameter)
Pm(xm,ym).
Can you take it from here and post the results for verification if you wish?
I am going to try to. How can I graph this so I can see it?
You can graph the two end points, then calculate the mid-point according to the given formula. Plot the mid-point and draw a circle with a radius equal to the length between the mid-point and one of the two ends. If the circle passes through both end-points of the diameter, and the mid-point falls on the diameter, your calculations are correct.
This is what I came up with, but I am still having a hard time graphing it.
Is this correct?
Mid-point formula =
(x1+x2)/2
(y1+y2/2
x = (4-4)/2 = 0
y = (-5 +1)/2 = -2
(0,-2) is the center??
Perfect!
Now give it a try to graph the points and the circle, if you could.
I did it! The center is (0,-2) on the graph after tracing the circle. Now i need help with the length of the radius of the circle. (Note that this is a distance.) Give the exact answer? What do I do here please? Thanks!
Here's a link to the graph that may help you do your own:
http://i263.photobucket.com/albums/ii157/mathmate/Jessica.jpg
The radius would be the distance between the centre and one of the two end-points.
The distance D between two known points P1(x1,y1) and P2(x2,y2) can be calculated using Pythagoras theorem:
D = sqrt((x2-x1)2+(y2-y1)2)
Now put P1 as one of the end-points of the diameter, and P2 as the centre of the circle that you have calculated, you should be able to find D.
The answer for the radius should be 5.
Don't see how you get 5?
How do you square 4? 4*4 = 16 correct? So then how can R = 5? I don't get it...Thanks by the way for the graph!
I think I see what you are now talkin about! is this correct?
D = sqrt ((x2-x1)2+ (y2-y1)2)
-4- -4 = -8
1- -5 = 6
Half the distance between the two given points
d = diameter = sqrt (82 + 62) =sqrt (64+36) = sqrt (100 = 10
Radius = 5
NOW i need to know how to put this in standard form? If this is correct?