Question

1. in the given figure, find the point x on the line segment that would partition the line segment into the ratio cx:xd = 2:5

Explanation:

Step1: Recall the section - formula

The formula to find the point \(x\) that divides the line - segment joining \(y_1\) and \(y_2\) in the ratio \(m:n\) is \(x=\frac{my_2 + ny_1}{m + n}\). Here, \(y_1=-7\), \(y_2 = 21\), \(m = 2\), and \(n = 5\).

Step2: Substitute the values into the formula

\[

$$\begin{align*} x&=\frac{2\times21+5\times(-7)}{2 + 5}\\ &=\frac{42-35}{7}\\ &=\frac{7}{7}\\ & = 1 \end{align*}$$

\]

Answer:

\(1\)