In the given figure A, B, C and D are collinear points. If AC = 3 cm, BD = 4 cm andBC = 2 cm, then AD is

1. Break Down the Problem

To find $AD$, we need to express it in terms of the given segments $AC$, $BD$, and $BC$.

2. Relevant Concepts

We know the distance between two points on a line can be calculated by adding or subtracting distances. We also recognize that the points A, B, C, and D are collinear.

3. Analysis and Detail

Given:

• $AC = 3 \, \text{cm}$
• $BC = 2 \, \text{cm}$
• $BD = 4 \, \text{cm}$

First, we can find $AB$ using the relationship: $AB = AC - BC$ Thus, substituting the values: $AB = 3 \, \text{cm} - 2 \, \text{cm} = 1 \, \text{cm}$

Next, we can express $AD$ as: $AD = AB + BD$ Now substituting the obtained value of $AB$: $AD = 1 \, \text{cm} + 4 \, \text{cm} = 5 \, \text{cm}$

4. Verify and Summarize

The calculations were carried out step by step, ensuring accuracy throughout. The derived measures of segment lengths were consistently verified through a logical progression based on the geometry of collinear points.

Final Answer

Therefore, the length of $AD$ is $5 \, \text{cm}$.