Question

WILL GIVE A MEDAL AND A FAN
Find the length of the diameter of a circle whose endpoints are at (11, 4) and (10, 5).

A. 1
B. square root 2
C. 2 square root 2

Answer 1

you have an equation for a circle
\[(x+k)^{2}+(y+k)^{2}=r^{2}\]

you have the end points of the diameter
(11,4) and (10,5)

you need to figure out the midpoint of the circle the equation for the midpoint is

\[(\frac{ x_{1}+x_{2} }{ 2 } , \frac{ y_{1}+y_{2} }{ 2})\]

then we would use the values for x and y, to replace K in the equation of the circle for example if I were to get the midpoint to be

(2,1)

then my circle equation would be

\[(x-2)^{2}+(y-1)^{2}=r^{2}\]

now we work out the radius which is the distance of the line equation

\[r=\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}}\]

then obviously the diameter is double the radius

this explanation shows how to write the entire equation of a circle from given points incase you need it in the future