Question

find the distance between points a and x.

Explanation:

Step1: Determine positions of A and X

From the number line, point A is at $\frac{1}{4}$? Wait, no, looking at the marks: 0, then A, then $\frac{1}{2}$, then X, then 1. Wait, the distance between 0 and $\frac{1}{2}$ is one segment, $\frac{1}{2}$ to 1 is another. Wait, actually, the marks: 0, then A (let's see, the first mark after 0 is A, then $\frac{1}{2}$, then X, then 1. So the distance between 0 and $\frac{1}{2}$ is $\frac{1}{2}$, so each small segment? Wait, no, the number line has 0, $\frac{1}{2}$, 1, $1\frac{1}{2}$, 2, $2\frac{1}{2}$. So the distance between 0 and $\frac{1}{2}$ is $\frac{1}{2}$, so the interval between 0 and $\frac{1}{2}$ is split into two parts? Wait, A is at $\frac{1}{4}$? No, wait, the points: A is at $\frac{1}{4}$? No, looking at the dots: A is at a position, X is at $\frac{3}{4}$? Wait, no, let's count the segments. From 0 to $\frac{1}{2}$: two small segments (since A is at the first, X at the second? Wait, no, the number line: 0, then A, then $\frac{1}{2}$, then X, then 1. So the distance from 0 to $\frac{1}{2}$ is $\frac{1}{2}$, so each small segment is $\frac{1}{4}$? Wait, no, maybe A is at $\frac{1}{4}$ and X is at $\frac{3}{4}$? Wait, no, let's check the positions. Wait, the number line has marks at 0, $\frac{1}{2}$, 1, $1\frac{1}{2}$, etc. So between 0 and $\frac{1}{2}$, there are two equal parts? So each part is $\frac{1}{4}$. So A is at $\frac{1}{4}$, X is at $\frac{3}{4}$? Wait, no, the dot for A is after 0, then a mark at $\frac{1}{2}$, then X, then 1. Wait, maybe the distance between A and X is the difference between their coordinates. Let's assume A is at $\frac{1}{4}$? No, wait, maybe the number line: 0, then A (at $\frac{1}{4}$), then $\frac{1}{2}$ (at $\frac{2}{4}$), then X (at $\frac{3}{4}$), then 1 (at $\frac{4}{4}$). Wait, no, the problem is to find the distance between A and X. Let's look at the number line: the distance between 0 and $\frac{1}{2}$ is $\frac{1}{2}$, so the segment from 0 to $\frac{1}{2}$ is divided into two equal parts, so each part is $\frac{1}{4}$. So A is at $\frac{1}{4}$, X is at $\frac{3}{4}$? Wait, no, maybe A is at $\frac{1}{4}$ and X is at $\frac{3}{4}$? Then the distance is $\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$? Wait, no, that can't be. Wait, maybe the number line: 0, then A (at $\frac{1}{4}$), then $\frac{1}{2}$ (at $\frac{2}{4}$), then X (at $\frac{3}{4}$), then 1 (at $\frac{4}{4}$). Wait, no, the distance between A and X: if A is at $\frac{1}{4}$ and X is at $\frac{3}{4}$, then the distance is $\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$. Wait, but maybe the positions are A at $\frac{1}{4}$? No, wait, the number line has 0, then a dot (A), then $\frac{1}{2}$, then a dot (X), then 1. So the distance from A to $\frac{1}{2}$ is $\frac{1}{4}$, and from $\frac{1}{2}$ to X is $\frac{1}{4}$, so total distance from A to X is $\frac{1}{4} + \frac{1}{4} = \frac{1}{2}$. Wait, that makes sense. So the distance between A and X is $\frac{1}{2}$.

Wait, maybe I misread. Let's see: the number line has 0, then A, then $\frac{1}{2}$, then X, then 1. So the distance between A and $\frac{1}{2}$ is $\frac{1}{4}$, and between $\frac{1}{2}$ and X is $\frac{1}{4}$, so total distance is $\frac{1}{4} + \frac{1}{4} = \frac{1}{2}$. Alternatively, if A is at $\frac{1}{4}$ and X is at $\frac{3}{4}$, then the distance is $\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$. So the distance is $\frac{1}{2}$.

Step1: Identify coordinates of A and X

From the number line, let's assume the unit between 0 and $\frac{1}{2}$ is divided into two equal parts. So A is at $\frac{1}{4}$? No, wait, maybe the marks: 0, then A (at $\frac{1}{4}$), then $\frac{1}{2}$ (at $\frac{2}{4}$), then X (at $\frac{3}{4}$), then 1 (at $\frac{4}{4}$). Wait, no, the distance between A and X: the difference between their x-coordinates. Let's say A is at $\frac{1}{4}$ and X is at $\frac{3}{4}$. Then distance is $|\frac{3}{4} - \frac{1}{4}| = \frac{2}{4} = \frac{1}{2}$.

Alternatively, maybe the number line has A at $\frac{1}{4}$ and X at $\frac{3}{4}$, so the distance is $\frac{1}{2}$.

Answer:

$\frac{1}{2}$