Question

on a number line, point s is located at - 3 and point t is located at 9. what is the location of point k on (overline{st}) given that the ratio of sk to kt is 3:4?

Explanation:

Step1: Use the section - formula

Let the location of point \(S = - 3\), the location of point \(T=9\), and the location of point \(K\) be \(x\). Given the ratio of \(SK\) to \(KT\) is \(3:4\). The section - formula for a point \(K\) that divides the line segment joining \(S(x_1)\) and \(T(x_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\). Here, \(x_1=-3\), \(x_2 = 9\), \(m = 3\), and \(n = 4\).

Step2: Substitute the values into the formula

\[

$$\begin{align*} x&=\frac{3\times9+4\times(-3)}{3 + 4}\\ &=\frac{27-12}{7}\\ &=\frac{15}{7} \end{align*}$$

\]

Answer:

None of the provided options (A, B, C, D) are correct as the correct value is \(\frac{15}{7}\)