a line segment AB has a length of 20 units.point C divides the line segment AB in the ratio 2:3

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.

A line segment AB has a length of 20 units. Point C divides the line segment AB in the ratio 2:3.

Learn how to divide a line segment of 20 units in the ratio 2:3, and calculate the lengths of segments AC and CB. This problem covers geometry concepts, ratio and proportion, and the section formula. Suitable for students in Grades 8-10.

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