If I know the diameter of a circle, is it possible to find coordinates on it? For my project I have 10 points evenly on the circumference of a circle that I need to find out the coordinates (x,y) for. Is there a formula? Thanks!
2007-12-18 07:08:53 · 2 answers · asked by Drizzle 2 in Science & Mathematics ➔ Mathematics
If you can choose your coordinate system, then the easiest way is to put the center of the circle at the origin (0, 0) (where the x and y-axes cross).
The coordinates of a point (x, y) on a circle of radius 5 are given by x = 5 cos θ, where θ is the angle between the line segment from (0, 0) to (x, y) and the x-axis.
If you put the first point on the x-axis (θ = 0), it will have coordinates (5, 0). Then each angle is 360°/10 = 36° more than the previous one. So the coordinates will be:
(5, 0), (5cos(36°), 5sin(36°)), (5cos(2*36°), 5sin(2*36°)), (5cos(3*36°), 5sin(3*36°)), ... , (5cos(9*36°), 5sin(9*36°))
You can use your calculator to get decimal approximations. The first few are:
(5, 0), (4.05, 2.94), (1.55, 4.76), (-1.55, 4.76), ...
Alternatively, if you're just trying to draw the points on the circle you can use a protractor to measure increments of 36 degrees on the circle...
2007-12-18 07:32:10 · answer #1 · answered by a²+b²=c² 4 · 1⤊ 0⤋
Think about any point (x, y). It will be a specified distance (r) from the center of the circle.
Take the center to be (a,b) and the radius to be r.
The general formula for a circle is:
(x - a)² + (y - b)² = r²
This comes directly from the Pythagorean Theorem.
Note, if you have a diameter, just cut it in half to get the radius... the equivalent formula for your case would be:
(x - a)² + (y - b)² = (d/2)²
2007-12-18 07:12:34 · answer #2 · answered by Puzzling 7 · 3⤊ 0⤋