1. If $a, b, c$ are distinct real numbers, and the coordinates of three points are $A(a+b, c), B(b+c, a), C(c+$ $a, b)$, then the positional relationship of these three points is ( ).
(A) on the same straight line
(B) form a right triangle
(C) form an obtuse triangle
(D) form an equilateral triangle
,- 1. (A).
$$
\begin{aligned}
\because A B & =\sqrt{(a-c)^{2}+(c-a)^{2}}=\sqrt{2}|a-c|, \\
A C & =\sqrt{(b-c)^{2}+(c-b)^{2}}=\sqrt{2}|b-c|, \\
B C & =\sqrt{(b-a)^{2}+(a-b)^{2}}=\sqrt{2}|a-b|,
\end{aligned}
$$

Without loss of generality, assume $a>b>c$, then
$$
A B=\sqrt{2}(a-c), A C=\sqrt{2}(b-c),
$$
$B C=\sqrt{2}(a-b)$. Thus, $A B-A C=B C$.
$\therefore A, B, C$ are collinear.