Answer: (-1, -7)
Explanation:
To find the coordinates of the point on the directed line segment from (-7, -10) to (1, -6) that partitions the segment into a ratio of 3 to 1, you can use the following formula:
\[P(x, y) = \left(\frac{{3x_2 + 1x_1}}{4}, \frac{{3y_2 + 1y_1}}{4}\right)\]
Where:
- (x, y) are the coordinates of the point we're trying to find.
- (x_1, y_1) are the coordinates of the starting point (-7, -10).
- (x_2, y_2) are the coordinates of the ending point (1, -6).
Now, plug in the values:
\[P(x, y) = \left(\frac{{3(1) + 1(-7)}}{4}, \frac{{3(-6) + 1(-10)}}{4}\right)\]
\[P(x, y) = \left(\frac{{3 - 7}}{4}, \frac{{-18 - 10}}{4}\right)\]
\[P(x, y) = \left(\frac{{-4}}{4}, \frac{{-28}}{4}\right)\]
\[P(x, y) = (-1, -7)\]
So, the coordinates of the point that partitions the segment into a ratio of 3 to 1 are (-1, -7).