To determine the inverse of a set of ordered pairs, such as $\{(-2, 3), (7, -10), (2, -3), (-7, 10)\}$, we need to swap the components in each pair.

Let's compute the inverse by swapping the elements of each pair:

1. Swap $(-2, 3)$ to $(3, -2)$,
2. Swap $(7, -10)$ to $(-10, 7)$,
3. Swap $(2, -3)$ to $(-3, 2)$,
4. Swap $(-7, 10)$ to $(10, -7)$.

Thus, the inverse is: $\{(3, -2), (-10, 7), (-3, 2), (10, -7)\}.$

The correct answer is the first option: $\{(3, -2), (-10, 7), (-3, 2), (10, -7)\}.$

Would you like further clarification or details on how to calculate the inverse of relations?

Here are 5 related questions to expand your understanding:

1. How do you determine the inverse of a relation in general?
2. What is the difference between an inverse relation and an inverse function?
3. Can every relation have an inverse?
4. How do inverses relate to graphs of relations?
5. What is the significance of a relation's inverse in real-world applications?

Tip: The inverse of a relation swaps the input and output, just like reflecting a graph across the line $y = x$.