Question

point w is located at (0, 7), and point x is located at (4, 0). julianne wants to find point f on $overline{wx}$ such that the ratio of wf to fx is 2:3.

Explanation:

Step1: Use section - formula

The section formula for a point \(F(x,y)\) that divides the line - segment joining \(W(x_1,y_1)\) and \(X(x_2,y_2)\) in the ratio \(m:n\) is given by \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(x_1 = 0,y_1 = 7,x_2 = 4,y_2 = 0,m = 2,n = 3\).

Step2: Calculate the x - coordinate of point F

\[x=\frac{2\times4+3\times0}{2 + 3}=\frac{8+0}{5}=\frac{8}{5}=1.6\]

Step3: Calculate the y - coordinate of point F

\[y=\frac{2\times0+3\times7}{2 + 3}=\frac{0 + 21}{5}=4.2\]

Answer:

The coordinates of point \(F\) are \((1.6,4.2)\)