Question

What are the coordinates of the point on the directed line segment from (-3,5) to (-1,- 7) that partitions the segment into a ratio of 3 to 1?

Answer 1

(-1.5,-4)

Step-by-step explanation:

Given the directed line segment from (-3,5) to (-1,- 7), the point that partitions the segment into a ratio of 3 to 1 can be found using the formula.

`(x,y)=((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n))`
`\begin{gathered} m\colon n=3\colon1 \\ (x_(1,)y_1)=(-3,5),\text{ }(x_(2,)y_2)=(-1,-7) \end{gathered}`

Therefore:

`\begin{gathered} (x,y)=((3(-1)+1(-3))/(3+1),(3(-7)+1(5))/(3+1)) \\ =((-3-3)/(4),(-21+5)/(4)) \\ =((-6)/(4),(-16)/(4)) \\ =(-1.5,-4) \end{gathered}`

The coordinates of the point on the directed line segment from (-3,5) to (-1,- 7) that partitions the segment into a ratio of 3 to 1 is (-1.5,-4).