Consider the points (4,-7) and (-6, 13).
(a) Find the midpoint. Show work.
(b) If the point you found in (a) is the center of a circle, and the other two points are points on the circle, find the length of the radius of the circle. Find the exact answer and simplify as much as possible. Show work.
(c) State the equation of the circle described above (in standard form).
(a) The mid-point between two points is:
(xm,ym) = ((x1+x2)/2,(y1+y2)/2) = ((4-6)/2,(13-7)/2) = (-1,3)
(b) The radius is the distance from the midpoint (center of the circle) to either point on the circle. The distance between the midpoint (-1,3) and (-6,13) is:
d = [ (x2-xm)2+(y2-ym)2 ]1/2 = [(-6+1)2+(13-3)2]1/2 = [25+100]1/2 = 5√5
(c) The standard form for a circle is:
(x-h)2 + (y-k)2 = r2
Where (h,k) = the center of the circle and r = its radius. Plug in the values from (a) and (b) to state the equation of the circle in this problem.