Question

point m lies on the line segment connecting $l(-4,2)$ and $n(2,-4)$. if $m$ partitions the segment in the ratio $1:2$, what are the coordinates of m
a. $(-2,0)$
b. $(-3,1)$
c. $(-1,-1)$
d. $(2,0)$

Explanation:

Step1: Recall section formula

For a point $M(x,y)$ partitioning segment $L(x_1,y_1)$ to $N(x_2,y_2)$ in ratio $m:n$,
$$x=\frac{mx_2+nx_1}{m+n}, \quad y=\frac{my_2+ny_1}{m+n}$$
Here, $L(-4,2)$, $N(2,-4)$, $m=1$, $n=2$.

Step2: Calculate x-coordinate of M

Substitute values into x-formula:
$$x=\frac{1\times2 + 2\times(-4)}{1+2}=\frac{2-8}{3}=\frac{-6}{3}=-2$$

Step3: Calculate y-coordinate of M

Substitute values into y-formula:
$$y=\frac{1\times(-4) + 2\times2}{1+2}=\frac{-4+4}{3}=\frac{0}{3}=0$$

Answer:

A. $(-2, 0)$