# coordinate geometry circle

• Nov 24th 2009, 03:37 PM
decoy808
coordinate geometry circle
use coordinate geometry to show that a circle, with its centre at O(2,1) can be drawn through the points A(5,5) B(6,-2) and C (-2,2)
what is the area of the circle?

do i need to draw or can i calculate?
• Nov 24th 2009, 04:35 PM
aidan
Quote:

Originally Posted by decoy808
use coordinate geometry to show that a circle, with its centre at O(2,1) can be drawn through the points A(5,5) B(6,-2) and C (-2,2)
what is the area of the circle?

do i need to draw or can i calculate?

Calculate!
Calculate the distance from the center of the circle to each of the points A,B,C.
IF they are the same then you have a common distance, which is the radius.

(Check your coordinates for point C.)
• Nov 24th 2009, 05:59 PM
Soroban
Hello, decoy808!

I believe there is a typo . . .

Quote:

Use coordinate geometry to show that a circle, with its centre at O(2,1)
can be drawn through the points A(5,5), B(6,-2), and C(-2,-2)
What is the area of the circle?

Use the Distance Formula to show that: . $OA \:=\:OB\:=\:OC$
. . That is, the center is equidistant from the three points.

That distance is the radius of the circle.
. . Now you can find the area of the circle, right?

• Nov 25th 2009, 01:05 AM
decoy808
yes there was a type error at c. should be(-2,-2)

i found the distances

pa=5
pb=7
pc=7

a=pi(r^2)
=3.14 x 7^2
=154

is this correct. many thanks
• Nov 25th 2009, 10:25 AM
bjhopper
coordinate geometry circle
posted by decoy808

It is much easier to plot the points on coordinate paper.You see that B and C are points on different radii.You erect the slope diagram for the corrected C and find a 3,4 5 right triangle so the radius is 5

bjh