Answer
collinear.
Work Step by Step
Step 1. Given $A(-2,-5),B(1,7),C(3,15)$, we have $d(AB)=\sqrt {(-2-1)^2+(-5-7)^2}=\sqrt {153}=3\sqrt {17}$
Step 2. We have $d(BC)=\sqrt {(3-1)^2+(15-7)^2}=\sqrt {68}=2\sqrt {17}$
Step 3. We have $d(AC)=\sqrt {(-2-3)^2+(-5-15)^2}=\sqrt {425}==5\sqrt {17}$
Step 4. Since $d(AC)= d(AB)+d(BC)$, the three points are collinear.
