To find the missing endpoint of a segment, we can use the midpoint formula. The formula is:

$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$

Here, $M = (-7, -3)$ is the midpoint, and $(x_1, y_1) = (0, 0)$ is one of the endpoints. Let the missing endpoint be $(x_2, y_2)$.

Using the midpoint formula, we can set up two equations:

$\frac{0 + x_2}{2} = -7 \quad \text{and} \quad \frac{0 + y_2}{2} = -3$

Solving for $x_2$ and $y_2$:

$x_2 = 2(-7) = -14 \quad \text{and} \quad y_2 = 2(-3) = -6$

So, the missing endpoint is $(-14, -6)$.

The correct answer from the options is $(-14, -6)$.

Would you like any further details or have any other questions?

Related Questions:

1. How do you derive the midpoint formula?
2. Can you solve for the missing endpoint if both endpoints are unknown, given only the midpoint?
3. How would you apply the midpoint formula in 3D geometry?
4. What are some real-world applications of the midpoint formula?
5. How can you check if a point is the true midpoint of a line segment?

Tip: Always double-check your coordinates when working with the midpoint formula, as small mistakes can lead to incorrect results!