Question

select the coordinates of point x on rs that is ⅙ of the distance from r to s. a) (3, -1⅓) b) (-3, 1⅓) c) (-3, -1⅓) d) (3, 1⅓) r(-4, 2) s(2, -2)

Explanation:

Step1: Recall the section - formula

If a point \(X(x,y)\) divides the line - segment joining \(R(x_1,y_1)\) and \(S(x_2,y_2)\) in the ratio \(m:n\), then \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\). Here, \(m = 1\) and \(n=5\), \(x_1=-4,y_1 = 2,x_2 = 2,y_2=-2\).

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

\[

$$\begin{align*} x&=\frac{1\times2+5\times(-4)}{1 + 5}\\ &=\frac{2-20}{6}\\ &=\frac{-18}{6}\\ &=-3 \end{align*}$$

\]

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

\[

$$\begin{align*} y&=\frac{1\times(-2)+5\times2}{1 + 5}\\ &=\frac{-2 + 10}{6}\\ &=\frac{8}{6}\\ &=1\frac{1}{3} \end{align*}$$

\]

Answer:

B. \((-3,1\frac{1}{3})\)