Final answer:
The question seems to be about finding the coordinates of a point that divides a line segment in a certain ratio using the section formula in coordinate geometry. However, the complete question seems to be missing, likely including the coordinates for the second endpoint of the segment, which are necessary to answer the question accurately.
Step-by-step explanation:
You are looking for the coordinates of a point that divides a segment in the ratio of 1 to 3. This problem is a classic example of using the section formula in coordinate geometry. Unfortunately, it seems like part of your question might be missing. Usually, two points (x1, y1) and (x2, y2) define a segment on a coordinate plane. The coordinates (9, -6) you've provided could represent one endpoint of the segment, but without the coordinates of the other endpoint or additional context, we cannot establish the exact division point's coordinates.
To divide a line segment in a given ratio, you can use the section formula. If you want to find a point that divides the segment connecting A(x1, y1) and B(x2, y2) internally in the ratio m:n, the coordinates of the dividing point (x, y) can be found using the following formula:
x = (mx2 + nx1) / (m + n)
y = (my2 + ny1) / (m + n)
For your specific question, you would need to know both endpoints of the line segment to apply this formula. Please provide the complete question with both coordinates so we can assist you further.