Question

refer to the coordinate grid. find point x on $overline{ab}$ such that the ratio of $ax$ to $xb$ is 1:3.

Explanation:

Step1: Recall section - formula

If a point $X(x,y)$ 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, assume $A=(x_1,y_1)$ and $B=(x_2,y_2)$, and $m = 1$, $n = 3$.
Let's assume $A$ is at $(-3,2)$ and $B$ is at $(5,2)$ (by observing the grid).

Step2: Calculate the x - coordinate of $X$

$x=\frac{1\times5+3\times(-3)}{1 + 3}=\frac{5-9}{4}=\frac{-4}{4}=-1$.

Step3: Calculate the y - coordinate of $X$

Since $A$ and $B$ have the same $y$ - coordinate ($y = 2$), $y=\frac{1\times2+3\times2}{1 + 3}=\frac{2 + 6}{4}=\frac{8}{4}=2$.

Answer:

The coordinates of point $X$ are $(-1,2)$.