Question 1136294

 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((1-(-7))^2+(5-9)^2)}}}
{{{d=sqrt((1+7)^2+(-4)^2)}}}
{{{d=sqrt(8^2+16)}}}
{{{d=sqrt(64+16)}}}
{{{d=sqrt(80)}}}
{{{d=4sqrt(5)}}}

(b) What is the center point C of the circle?
the center point C of the circle is midpoint of  the diameter; 

({{{(1+(-7))/2}}}, {{{(5+9)/2}}})=({{{-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}}})



{{{drawing ( 600,600, -10, 10, -5, 15,

circle(-3,7,.12),circle(-3,7,2sqrt(5)),locate(-3,7,C(-3,7)),
circle(1,5,.12),circle(-7,9,.12),locate(1,5,p(1,5)),locate(-7,9,p(-7,9)),
graph( 600,600, -10, 10, -5, 15,0)) }}}