Question

what are the coordinates of the point on the directed line segment from (-7, -4) to (2, -10) that partitions the segment into a ratio of 1 to 2?

Explanation:

Step1: Use the section - formula for x - coordinate

The formula for the x - coordinate of a point that divides the line segment joining $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ is $x=\frac{mx_2+nx_1}{m + n}$. Here, $x_1=-7$, $x_2 = 2$, $m = 1$, and $n = 2$.
$x=\frac{1\times2+2\times(-7)}{1 + 2}=\frac{2-14}{3}=\frac{-12}{3}=-4$

Step2: Use the section - formula for y - coordinate

The formula for the y - coordinate of a point that divides the line segment joining $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ is $y=\frac{my_2+ny_1}{m + n}$. Here, $y_1=-4$, $y_2=-10$, $m = 1$, and $n = 2$.
$y=\frac{1\times(-10)+2\times(-4)}{1 + 2}=\frac{-10 - 8}{3}=\frac{-18}{3}=-6$

Answer:

$(-4,-6)$