The point(-2,5) is on a circle that has a center(5, -3).Find the diameter of the circle?

Answer 1

we can use the formula distance between two points on this one...

d^2 = (x2 - x1)^2 + (y2 - y1)^2

d^2 = (5 - -2)^2 + (-3 - 5)^2

d^2 = 49 + 64

d^2 = 113

d = sqrt of 113 = radius

diameter is equal to 2 x radius therefore:

D = 2(sqrt of 113)

D = 21.26 units

Answer 2

For this, realize that the two points can be used to form a right triangle with hypotenuse R^2 = X^2 + Y^2; where X = (x1 - x0) and Y = (y1 - y0) and p1 = (-2,5) = (x1,y1) and p0 = (5.-3) = (x0,y0). That hypotenuse is the radius of your circle. Thus, 2R = D, the diameter you are looking for.

So X = x1 - x0 = -2 - 5 = -7 and X^2 = 49
Y = y1 - y0 = 5 - (-3) = 8 and Y^2 = 64

Then R^2 = 49 + 64 = 113 and R = sqrt(113) so that D = 2R = 2 sqrt(113), which is your diameter of the circle.

The lesson here is that one can always, without exception, fashion a right triangle whose hypoteneuse is the radius of a circle and whose value is the square root of the sum of the squares of the X distance and Y distance between a point on the center and a point on the circumference of that circle.

Answer 3

Diameter = 2 * [ (5 - -2)^2 + (-3 -5)^2]^1/2
= 33.1