Consider the points 6 3 and 2 11 State the midpoint of the l

Consider the points (–6, 3) and (–2, 11).

State the midpoint of the line segment with the given endpoints.  

If the point you found in (a) is the center of a circle and the other two points are on the circle, find the length of the radius of the circle. That is, find the distance between the center point and a point on the circle. Find the exact answer and simplify as much as possible. Show work.

Solution

given points (–6, 3) and (–2, 11).   

mid point of line joining (a,b) ,(c,d) is ((a+c)/2, (b+d)/2)

mid point of line joining (–6, 3) and (–2, 11). is ((-6-2)/2, (3+11)/2)

mid point of line joining  (–6, 3) and (–2, 11). is (-4, 7)

centre of circle is (-4, 7)

distance between the center point (-4, 7) and a point on the circle(–6, 3) is radius

radius =[((-6)-(-4))²+(3-7)²]

radius =[(-2)²+(-4)²]

radius =[4+16]

radius =20

radius =25