Final answer:
The coordinates of the point that partitions the directed line segment from (3,3) to (10,-4) in a 5 to 2 ratio are (8, -2).
Step-by-step explanation:
To find the coordinates of the point that partitions the directed line segment from (3,3) to (10,-4) in a ratio of 5 to 2, we use the section formula for internal division. Given the partition ratio of m:n, the coordinates of the point can be found using the following expressions:
- x-coordinate = (m × x2 + n × x1) / (m + n)
- y-coordinate = (m × y2 + n × y1) / (m + n)
Here, we substitute m = 5, n = 2, (x1, y1) = (3, 3), and (x2, y2) = (10, -4) into the formula.
x-coordinate = (5 × 10 + 2 × 3) / (5 + 2) = (50 + 6) / 7 = 56 / 7 = 8
y-coordinate = (5 × -4 + 2 × 3) / (5 + 2) = (-20 + 6) / 7 = -14 / 7 = -2
Therefore, the coordinates of the required point are (8, -2).