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

Answer:

(-1.5,-4)

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)=(\frac{mx_2+nx_1}{m+n},\frac{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:

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

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).