Question

find the coordinate of point c on $overline{ab}$ such that the ratio of ac to cb is 3:6. point c is located at __. a) $(-3\frac{1}{3}, - 6)$ b) $(1,1)$ c) $(-1,-2)$ d) $(6,8)$

Explanation:

Step1: Recall the section - formula

If a point $C(x,y)$ 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, $m = 3$ and $n = 6$, so the ratio $m:n=3:6 = 1:2$.
Let's assume the coordinates of $A$ are $(-4,-6)$ and the coordinates of $B$ are $(5,6)$ (by observing the graph).

Step2: Calculate the x - coordinate of point C

$x=\frac{1\times5+2\times(-4)}{1 + 2}=\frac{5-8}{3}=\frac{-3}{3}=-1$.

Step3: Calculate the y - coordinate of point C

$y=\frac{1\times6+2\times(-6)}{1 + 2}=\frac{6 - 12}{3}=\frac{-6}{3}=-2$.

Answer:

C. $(-1,-2)$