Question

the point b lies on the segment $overline{ac}$. find the coordinates of b so that the ratio of ab to bc is 6 to 1. a (-13,20) b (?,?) c (1,-1)

Explanation:

Step1: Recall section - formula

If a point $B(x,y)$ divides the line - segment joining $A(x_1,y_1)$ and $C(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $x_1=-13,y_1 = 20,x_2 = 1,y_2=-1,m = 6,n = 1$.

Step2: Calculate the x - coordinate of B

$x=\frac{6\times1+1\times(-13)}{6 + 1}=\frac{6-13}{7}=\frac{-7}{7}=-1$.

Step3: Calculate the y - coordinate of B

$y=\frac{6\times(-1)+1\times20}{6 + 1}=\frac{-6 + 20}{7}=\frac{14}{7}=2$.

Answer:

$(-1,2)$