Question

the point b lies on the segment $overline{ac}$. find the coordinates of b so that the ratio of ab to bc is 5 to 2. c (28, 12) b (?,?) a (-7, -2) coordinates of b :

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, $x_1=-7,y_1=-2,x_2 = 28,y_2 = 12,m = 5,n = 2$.

Step2: Calculate the x - coordinate of B

$x=\frac{5\times28+2\times(-7)}{5 + 2}=\frac{140-14}{7}=\frac{126}{7}=18$.

Step3: Calculate the y - coordinate of B

$y=\frac{5\times12+2\times(-2)}{5 + 2}=\frac{60 - 4}{7}=\frac{56}{7}=8$.

Answer:

$(18,8)$