Question

point a is at (2, -8) and point c is at (-4, 7). find the coordinates of point b on $overline{ac}$ such that the ratio of ab to bc is 2 : 1. b = ( , )

Explanation:

Step1: Use the section - formula for x - coordinate

The formula for the x - coordinate of a point \(B(x,y)\) that divides the line segment joining \(A(x_1,y_1)\) and \(C(x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\). Here, \(x_1 = 2,y_1=-8,x_2=-4,y_2 = 7,m = 2,n = 1\).

$$x=\frac{2\times(-4)+1\times2}{2 + 1}=\frac{-8 + 2}{3}=\frac{-6}{3}=-2$$

Step2: Use the section - formula for y - coordinate

The formula for the y - coordinate of the point \(B\) is \(y=\frac{my_2+ny_1}{m + n}\).

$$y=\frac{2\times7+1\times(-8)}{2 + 1}=\frac{14-8}{3}=\frac{6}{3}=2$$

Answer:

\((-2,2)\)