Question

The point (4,5) lies on a circle. What is

the diameter of this circle if the center is
located at (7,9)

Answer 1

well, we know the center of the circle is at (7 , 9), and we also know that a point right on the circle is at (4 ,5), now, the distance between those two points is simply the radius, keeping in mind that the diameter is simply twice the radius

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{7}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{5})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ \stackrel{radius}{r}=√((~~4 - 7~~)^2 + (~~5 - 9~~)^2) \implies r=√((4 -7)^2 + (5 -9)^2) \\\\\\ r=√(( -3 )^2 + ( -4 )^2) \implies r=√( 9 + 16 ) \implies r=5~\hfill \underset{diameter}{\stackrel{2(5)}{10}}`