Question

refer to the coordinate grid. find x on $overline{mn}$ that is $\frac{3}{4}$ of the distance from m to n.

Explanation:

Step1: Identify coordinates of M and N

Let's assume $M(- 5,-4)$ and $N(5,4)$.

Step2: Use the section - formula

The section - formula for a point $X(x,y)$ that divides the line segment joining $M(x_1,y_1)$ and $N(x_2,y_2)$ in the ratio $m:n$ is given by $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $m = 3$ and $n=1$.
For the x - coordinate of $X$:
$x=\frac{3\times5+1\times(-5)}{3 + 1}=\frac{15 - 5}{4}=\frac{10}{4}=\frac{5}{2}$
For the y - coordinate of $X$:
$y=\frac{3\times4+1\times(-4)}{3 + 1}=\frac{12-4}{4}=\frac{8}{4} = 2$

Answer:

$X(\frac{5}{2},2)$