AB is the diameter of a circle where the coordinates of a and b are (-7,-9) (1,-5) respectively the coorsinates of the centre of the circle are 

The center of a circle that has a diameter AB can be found by calculating the midpoint of the points A and B.

Given:
- Coordinates of \( A(-7, -9) \)
- Coordinates of \( B(1, -5) \)

The formula to find the midpoint (which is the center of the circle) is:

\[
\text{Midpoint} = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)
\]

Substituting the given values:

\[
\text{Midpoint} = \left(\frac{-7 + 1}{2}, \frac{-9 + (-5)}{2}\right)
\]

\[
\text{Midpoint} = \left(\frac{-6}{2}, \frac{-14}{2}\right)
\]

\[
\text{Midpoint} = (-3, -7)
\]

So, the coordinates of the center of the circle are \( (-3, -7) \).

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How do you calculate the radius of the circle given points A and B?
2. What is the equation of the circle given its center and a point on the circle?
3. How do you find the equation of a line perpendicular to AB passing through the center?
4. What is the length of the diameter AB?
5. How do you find the area of the circle with the given diameter?

**Tip:** Midpoints are not only useful for finding the center of a circle but also for dividing line segments into equal parts!

Learn how to find the center of a circle with diameter AB given the coordinates (-7, -9) and (1, -5). The midpoint formula is used to determine the center coordinates (-3, -7). Suitable for students in Grades 7-9.

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