Given that the points are equally spaced, we know that $b=-a$, and $c=2 b$.
Since we need to select all true statements, let's examine each of them one by one.

(1) $\(b-c=a\)$

We can see graphically that this must be true. Since $b$ is one unit away from the origin and $c$ is two units away, subtracting $c$ from $b$ yields a result one unit away from the origin: $a$.
To confirm by doing the math, $\(b-c=b-2 b =-b=a\)$. True.

(2) The distance from $A$ to $C=3 b$

Don't be tricked: just because the points on the line are equally spaced, and $B$ is one unit away from the origin, doesn't mean the distance between each of them is $b!$ The distance from the origin to $B$, which is also the distance from the origin to $A$ or from $B$ to $C$, is not $b$ but rather $b \sqrt{2}$-remember the Pythagorean theorem. Therefore the distance from $A$ to $C$ is actually $\(3 b \sqrt{2}\)$, not $3 b$. False.

(3) $\(b a-c a>0\)$
ba is negative, as is ca, but which has the greater absolute value? Graphically, clearly $|c a|>|b a|$, so subtracting the larger negative number will yield a result that is positive.

Mathematically, $\(b a-c a=a(b-c)\)$, where $b-c$ is negative and so is $a$, so the product will be positive. True.
You could also evaluate each of these statements by substituting acceptable values for the coordinates of each point-for example, $A$ could be $(-1,-1), B$ could be $(1,1)$, and $C$ could be $(2,2)$-and then calculate the results for each statement.