If point ‘C’ lies between two points A and B such that AC = BC, thenAC = 1/4ABAC = 1/3ABAC = 3/4ABAC = 1/2AB

To solve this problem, we will analyze the relationship between points A, B, and C based on the information given. We know that point C lies between points A and B and that AC = BC.

1. ### Break Down the Problem

We need to determine the correct expression for AC in relation to AB, given that AC = BC.

2. ### Relevant Concepts

Let:

• $A$ be the position of point A,
• $B$ be the position of point B,
• $C$ be the position of point C.

Since C is between A and B, we can express the distances as:

• $AC = x$
• $BC = x$

From this, we can express the total distance AB as: $AB = AC + BC = x + x = 2x$

3. ### Analysis and Detail

We need to relate $AC$ to $AB$. Since $AB = 2x$, we can express $AC$ in terms of $AB$: $AC = x = \frac{1}{2}(AB)$ So, we know that $AC$ is half of $AB$.

4. ### Verify and Summarize

We found that: $AC = \frac{1}{2}AB$ Thus, the correct option from the choices given is $AC = \frac{1}{2}AB$.

Final Answer

The correct relationship is: $AC = \frac{1}{2}AB$