• Jun 20th 2009, 04:37 AM
Joker37
The points (8, 4) and (2, 2) are the ends of a diameter of a circle. Find the coordinates of the centre and the radius.

I know the centre is (5, 3) ...but how do you find out the radius?
• Jun 20th 2009, 04:52 AM
yeongil
Quote:

Originally Posted by Joker37
The points (8, 4) and (2, 2) are the ends of a diameter of a circle. Find the coordinates of the centre and the radius.

I know the centre is (5, 3) ...but how do you find out the radius?

Use the distance formula:
$\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let the (2, 2) be the point (x1, y1) and (8, 4) be (x2, y2):

\displaystyle \begin{aligned} d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \\ d &= \sqrt{(8 - 2)^2 + (4 - 2)^2} \\ d &= \sqrt{6^2 + 2^2} \\ d &= \sqrt{40} \\ d &= 2\sqrt{10} \\ \end{aligned}

Now, this is the diameter, so take half of that to get the radius:
$\displaystyle r = \sqrt{10}$

01
• Jun 20th 2009, 05:12 AM
Joker37
Quote:

Originally Posted by yeongil
Use the distance formula:
$\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Forgot about the distance formula. (Doh)