Question

1. point x on $overline{rs}$ is $\frac{1}{6}$ of the distance from r to s.

r(-4, 2)
s(2, -2)

Explanation:

Step1: Use the section - formula

The section - formula for a point \(X(x,y)\) that divides the line - segment joining \(R(x_1,y_1)\) and \(S(x_2,y_2)\) 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, \(m = 1\), \(n=5\), \(x_1=-4\), \(y_1 = 2\), \(x_2 = 2\), and \(y_2=-2\).

Step2: Calculate the x - coordinate of point \(X\)

\[x=\frac{1\times2+5\times(-4)}{1 + 5}=\frac{2-20}{6}=\frac{-18}{6}=-3\]

Step3: Calculate the y - coordinate of point \(X\)

\[y=\frac{1\times(-2)+5\times2}{1 + 5}=\frac{-2 + 10}{6}=\frac{8}{6}=\frac{4}{3}\]

Answer:

The coordinates of point \(X\) are \((-3,\frac{4}{3})\)