Final answer:
The coordinates of the point that partitions the line segment from (-6,-6) to (1,1) into a ratio of 1 to 6 are (-5/7, -5/7).
Step-by-step explanation:
The student asked for the coordinates of the point on the directed line segment from (-6,-6) to (1,1) that partitions the segment into a ratio of 1 to 6. To find this, we use the formula for section formula in the coordinate geometry which is (x, y) = ((mx2 + nx1)/(m + n), (my2 + ny1)/(m + n)), where (x1, y1) and (x2, y2) are the endpoints of the segment and m:n is the given ratio.
Substituting the values into the section formula, we get:
- x-coordinate = ((6*1 + (-6))/(6+1)), which simplifies to -5/7
- y-coordinate = ((6*1 + (-6))/(6+1)), which is also -5/7
So, the coordinates of the partition point are (-5/7, -5/7).