Given that point $C$ divides the line segment $AB$ in the ratio 2:3, the total ratio is 5 parts (2 + 3). The segment $AB$ has a total length of 20 units.

To find the length of segments $AC$ and $CB$:

1. Length of $AC$ (which corresponds to the 2 parts): $AC = \frac{2}{5} \times 20 = 8 \text{ units}$

2. Length of $CB$ (which corresponds to the 3 parts): $CB = \frac{3}{5} \times 20 = 12 \text{ units}$

Thus, point $C$ divides $AB$ into:

• $AC = 8$ units
• $CB = 12$ units

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you find the coordinates of $C$ given $A$ and $B$'s coordinates?
2. What is the midpoint formula for a line segment?
3. How do you generalize division of a line segment in a given ratio?
4. How can we apply this concept to a 3D line segment?
5. What is the difference between external and internal division of a line segment?

Tip: When dividing a line segment in a given ratio, always ensure the sum of the parts matches the total length of the segment.