Question

What are the coordinates of the point on the directed line segment from (-3, -9) to (4, 5) that partitions the segment into a ratio of 5 to 2?

Answer 1

the coordinates the partitions point is (x,y), and given m =5 and n = 2, then

for x

$\begin{gathered} x=\frac{m(x2)+n(x1)}{m+n} \\ x=\frac{5(4)+2(-3)}{5+2} \\ x=\frac{20-6}{7} \\ x=\frac{14}{7} \\ x=2 \end{gathered}$

for y

$\begin{gathered} y=\frac{m(y2)+n(y1)}{m+n} \\ y=\frac{5(5)+2(-9)}{5+2} \\ y=\frac{25-18}{7} \\ y=\frac{7}{7} \\ y=1 \end{gathered}$

answer: the coordinates are (2,1)