If the distance between two points is 1 cm on a 1:50 000 map, what would the distance in cm on a 1:10 000 map be? Answer is __ cm.

A map scale of $1:50\,000$ means that 1 cm on the map represents $50\,000$ cm in the real world.
Given map distance = 1 cm.

$$\text{Actual ground distance} = \text{Map distance} \times \text{Scale factor}$$ $$\text{Actual ground distance} = 1 \text{ cm} \times 50\,000 = 50\,000 \text{ cm}$$

A map scale of $1:10\,000$ means that 1 cm on this map represents $10\,000$ cm in the real world. We need to find out how many cm on this map would represent the actual ground distance of $50\,000$ cm.

$$\text{Distance on new map} = \frac{\text{Actual ground distance}}{\text{New map scale factor}}$$ $$\text{Distance on new map} = \frac{50\,000 \text{ cm}}{10\,000} = 5 \text{ cm}$$

The distance on a $1:10\,000$ map would be $\boxed{\text{5 cm}}$.