To find the coordinates of the other endpoint, let's denote the unknown endpoint as $(x, y)$.

Given:

• Midpoint $(x_m, y_m) = (-10, 15)$
• Known endpoint $(x_1, y_1) = (-9, 18)$

The midpoint formula is given by: $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) = (x_m, y_m)$

Using this formula, we can set up the following equations: $\frac{-9 + x}{2} = -10$ $\frac{18 + y}{2} = 15$

Now, solve each equation for $x$ and $y$:

Solving for $x$:

$\frac{-9 + x}{2} = -10$ Multiply both sides by 2: $-9 + x = -20$ Add 9 to both sides: $x = -11$

Solving for $y$:

$\frac{18 + y}{2} = 15$ Multiply both sides by 2: $18 + y = 30$ Subtract 18 from both sides: $y = 12$

Thus, the coordinates of the other endpoint are $(-11, 12)$.

Would you like more details on how these calculations were done, or do you have any other questions?

Here are some related questions you might find interesting:

1. How do you derive the midpoint formula?
2. Can you find the distance between the two endpoints using their coordinates?
3. How would the midpoint formula change in three-dimensional space?
4. What are some real-world applications of finding midpoints?
5. How can you verify that $(-11, 12)$ is indeed the correct endpoint?

Tip: When solving midpoint problems, always double-check your equations by plugging the coordinates back into the midpoint formula.