What are the coordinates of the point on the directed line segment from (1,-5) to(10, 1) that partitions the segment into a ratio of 1 to 5?

Using the section formula directly,

The required point is \(\left(\dfrac{5(1) + 1(10)}{5 + 1}, \dfrac{5(-5) + 1(1)}{5 + 1}\right) = \left(\dfrac{5}{2}, -4\right)\)

Thanks Max,

I can never remember the formula so here is my method

I look at the x's and y's separately

x's

10-1=9

9/6=1.5

1+1.5=2.5

y's

1--5=6

6/6=1

-5+1=-4

(2,5,-4)