Question

find the coordinates of point b on $overline{ac}$ such that the ratio of $overline{ab}$ to $overline{bc}$ is 3:1. a(-11,8) c(-3,0)

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, \(A(-11,8)\), \(C(-3,0)\), \(m = 3\), and \(n = 1\).

Step2: Calculate the x - coordinate of point B

\[x=\frac{3\times(-3)+1\times(-11)}{3 + 1}=\frac{-9-11}{4}=\frac{-20}{4}=-5\]

Step3: Calculate the y - coordinate of point B

\[y=\frac{3\times0+1\times8}{3 + 1}=\frac{0 + 8}{4}=2\]

Answer:

\((-5,2)\)