Question 1126048
given: Points ({{{5}}}, {{{2}}}) and ({{{8}}}, {{{-7}}}) 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.

since given points are endpoints of the diameter of a circle, the length of the diameter will be equal to the distance between these two points

use distance formula for ({{{5}}}, {{{2}}}) and ({{{8}}}, {{{-7}}})



{{{d=sqrt((x[2]-x[1])^2+(y[2]-y[1])^2)}}}

{{{d=sqrt((8-5)^2+(-7-2)^2)}}}

{{{d=sqrt(3^2+(-9)^2)}}}

{{{d=sqrt(9+81)}}}

{{{d=sqrt(90)}}}

{{{d=sqrt(9*10)}}}

{{{d=3sqrt(10)}}} approximately {{{9.48}}}->{{{r=4.74}}}


(b) 

What is the center point {{{C}}} of the circle?
the center point {{{C}}} of the circle will be midpoint line segment with given points as endpoints

({{{(5+8)/2}}}, {{{(2-7)/2}}}) 
=({{{13/2}}}, {{{-5/2}}}) 

so,  the center point {{{C}}} of the circle is at ({{{13/2}}}, {{{-5/2}}}) 


(c) 
Given the point {{{C}}} you found in part (b), state the point symmetric to {{{C}}} about the x-axis. 

both given points are symmetric to {{{C}}} about the x-axis

{{{ drawing( 600, 600, -15, 15, -15, 15,
circle(5,2,.12),circle(8,-7,.12),
locate(5,2,p(5,2)),locate(8,-7,p(8,-7)),circle(13/2,-5/2,4.74),
locate(13/2,-5/2,p(13/2,-5/2)),circle(13/2,-5/2,.12),
 graph( 600, 600, -15, 15, -10, 15, 0)) }}}