Question

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

Explanation:

Step1: Recall the 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, $m = 1$, $n = 6$, $x_1=-1$, $y_1 = 1$, $x_2=13$, and $y_2=-20$.

Step2: Calculate the x - coordinate of B

$x=\frac{1\times13+6\times(-1)}{1 + 6}=\frac{13-6}{7}=\frac{7}{7}=1$.

Step3: Calculate the y - coordinate of B

$y=\frac{1\times(-20)+6\times1}{1 + 6}=\frac{-20 + 6}{7}=\frac{-14}{7}=-2$.

Answer:

$(1,-2)$