Question

1. in the figure, the endpoints of the line segment are -9 and 13. determine the point x on the line segment that would partition the line segment into the ratio 7:11.

Explanation:

Step1: Recall the section - formula

The formula to find the point \(x\) that divides the line - segment with endpoints \(x_1\) and \(x_2\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\). Here, \(x_1=-9\), \(x_2 = 13\), \(m = 7\), and \(n = 11\).

Step2: Substitute the values into the formula

\[

$$\begin{align*} x&=\frac{7\times13+11\times(-9)}{7 + 11}\\ &=\frac{91-99}{18}\\ &=\frac{-8}{18}\\ &=-\frac{4}{9} \end{align*}$$

\]

Answer:

\(-\frac{4}{9}\)