Question

what are the coordinates of the point on the directed line segment from (-5, -2) to (7, 6) that partitions the segment into a ratio of 3 to 5?

Explanation:

Step1: Recall the section - formula

If a point $P(x,y)$ divides the line - segment joining $A(x_1,y_1)$ and $B(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $(x_1,y_1)=(-5,-2)$, $(x_2,y_2)=(7,6)$, $m = 3$, and $n = 5$.

Step2: Calculate the x - coordinate

$x=\frac{3\times7+5\times(-5)}{3 + 5}=\frac{21-25}{8}=\frac{-4}{8}=-\frac{1}{2}$

Step3: Calculate the y - coordinate

$y=\frac{3\times6+5\times(-2)}{3 + 5}=\frac{18 - 10}{8}=\frac{8}{8}=1$

Answer:

$(-\frac{1}{2},1)$