Answer:
The length of the diameter of the circle is 10 unit.
Step-by-step explanation:
Given : The center of a circle is at the origin. An endpoint of a diameter of the circle is at (-3, -4).
To find : How long is the diameter of the circle?
Solution :
The center of a circle is at the origin i.e. \(C=(x_1,y_1)=(0,0)\)
An endpoint of a diameter of the circle is at \(D=(x_2,y_2)=(-3,-4)\)
The distance between the center and the end point of the diameter is the radius of the circle.
So, we find the radius with the help of distance formula,
\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
Substitute the value in the formula,
\(r=\sqrt{(-3-0)^2+(-4-0)^2}\)
\(r=\sqrt{9+16}\)
\(r=\sqrt{25}\)
\(r=5\)
Diameter is twice of radius \(d=5\times 2=10\)
Therefore, The length of the diameter of the circle is 10 unit.
