Question

The center of a circle is at t he origin. An endpoint of a diameter of the circle is at (-3, -4). How long is the diameter of the circle?

step by step please

Answer 1

The center is the origin O(0,0). The point A(-3,-4) is from the circle since it is an endpoint of a diameter. So the diameter of the circle is :
\[d=2r=2AO\]
where r is the radius !
So, we calculate AO :
\[AO=\sqrt{(x_A-x_O)^2-(y_A-y_O)^2}=\sqrt{(-3)^2+(-4)^2}=5\]
So :
\[d=2\times 5=10\]

Answer 2

thank you so much! very helpful!