The problem is asking to find the coordinates of point $M$, given that segment $AM$ is a median of triangle $ABC$.

Key Information:

• $A(-9, 6)$
• $B(7, -5)$
• $C(-13, -2)$
• $AM$ is a median, so $M$ is the midpoint of side $BC$.

Step-by-step solution:

1. Find the coordinates of $M$, the midpoint of segment $BC$: The midpoint formula is: $M\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$ where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of points $B$ and $C$.

   Plugging in the coordinates of $B(7, -5)$ and $C(-13, -2)$: $M_x = \frac{7 + (-13)}{2} = \frac{-6}{2} = -3$ $M_y = \frac{-5 + (-2)}{2} = \frac{-7}{2} = -3.5$

Thus, the coordinates of point $M$ are $(-3, -3.5)$.

Final Answer:

The coordinates of point $M$ are $(-3, -3.5)$.

Would you like further clarification or details?

Here are 5 related questions to expand on this topic:

1. How would you find the length of the median $AM$?
2. How do you calculate the centroid of triangle $ABC$?
3. What is the equation of the line passing through points $A$ and $M$?
4. Can you determine if triangle $ABC$ is isosceles based on its coordinates?
5. How would you find the area of triangle $ABC$ using its vertices?

Tip: Remember that the centroid of a triangle, where all three medians meet, divides each median into a 2:1 ratio.