SOLUTION: 23. Points (1, 5) and ( - 7, 9) are endpoints of the diameter of a circle. (a) What is the length of the diameter? Give the exact answer, simplified as much as possible. Show w

Algebra ->  Equations -> SOLUTION: 23. Points (1, 5) and ( - 7, 9) are endpoints of the diameter of a circle. (a) What is the length of the diameter? Give the exact answer, simplified as much as possible. Show w      Log On


   

Question 1136294: 23. Points (1, 5) and ( - 7, 9) are endpoints of the diameter of a circle.
(a) What is the length of the diameter? Give the exact answer, simplified as much as possible.
Show work.
(b) What is the center point C of the circle?
(c) Given the point C you found in part (b), state the point symmetric to C about the y-axis.

Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

Points (1, 5) and (+-+7,+9) are endpoints of the diameter of a circle.
(a) What is the length of the diameter?
the length of the diameter equals to the distance between given points and it is
d=sqrt%28%281-%28-7%29%29%5E2%2B%285-9%29%5E2%29
d=sqrt%28%281%2B7%29%5E2%2B%28-4%29%5E2%29
d=sqrt%288%5E2%2B16%29
d=sqrt%2864%2B16%29
d=sqrt%2880%29
d=4sqrt%285%29
(b) What is the center point C of the circle?
the center point C of the circle is midpoint of the diameter;
(%281%2B%28-7%29%29%2F2, %285%2B9%29%2F2)=(-3, 7)
the center point C of the circle is at (-3, 7)
(c) Given the point C you found in part (b), state the point symmetric to C about the y-axis.
the point symmetric to C about the y-axis is (3, 7)