The ratio of 1 to 2 means that the length of the line segment from the starting point to the partition point is one-third of the total length of the segment.
Using the distance formula, we find that the length of the line segment from (-6,-4) to (3,-1) is $\sqrt{(-6-3)^2 + (-4-(-1))^2} = \sqrt{81+9} = \sqrt{90} = 3\sqrt{10}.$ The partition point is located $\frac{1}{3}$ of this distance away from the starting point.
Therefore, the coordinates of the partition point can be found by finding $\frac{1}{3}$ of the difference between the coordinates of the two points.
The x-coordinate of the partition point is $\frac{1}{3} (3 - (-6)) = \frac{1}{3} (9) = 3.$
The y-coordinate of the partition point is $\frac{1}{3}((-1) - (-4)) = \frac{1}{3}(3) = 1.$
Therefore, the coordinates of the partition point are $\boxed{(3,1)}.$
[asy]
unitsize(0.5 cm);
draw((-7,0)--(4,0));
draw((0,-5)--(0,2));
draw((-6,-4)--(3,-1),red);
draw((0,0)--(3,0),Arrow(6));
draw((0,0)--(0,1),Arrow(6));
dot("$(3,1)$",(3,1),NE);
dot("$(3,0)$",(3,0),SE);
[/asy]
What are the coordinates of the point on the directed line segment from (−6,−4) to (3,−1) that partitions the segment into a ratio of 1 to 2?
1 answer