Question

Given a circle with endpoints of a diameter at –10 – 1i and 6 + 11i, answer the questions below. 1. The center of the circle is

Answer 1

1.) (-2+5i)

2.) 10 units

3.) 4+13i & 8+5i

Answer 2

The given endpoints which are in imaginary number can be written in Cartesian coordinates form as:

–10 – 1 i = (- 10, - 1)

6 + 11 i = (6, 11)

Since we know that these are the endpoints of the diameter, then this must mean that the center of the circle is the point located in the middle of the endpoints. So we use the middle distance formula to calculate for the coordinates of the center:

x = (-10 + 6) / 2 = - 4 / 2 = -2

y = (- 1 + 11) / 2 = 10 / 2 = 5

 

So the center is located at:

(- 2, 5)