The center of a circle is at the origin. and end point of a diameter of the circle is at (-3,-4) how long is the diameter of the circle

10 units long

Step-by-step explanation:

We need to find the distance from the origin (0, 0) to the point (-3, -4), that will be a radius of the circle.  

Use the distance formula:  d = √[(x2 - x1)² + (y2 - y1)²]  

Plug in the values from the 2 points we are given...

d = √[(-3 - 0)² + (-4 - 0)²]

    d = √[(-3)² + (-4)²]

        d = √[ 9 + 16 ]

              d = √25

                     d = 5

The radius is 5, therefore the diameter is 10.  (the diameter is always twice the length of the radius)