Question

refer to the number line. find the coordinate of point x such that the ratio of bx to xf is 3:2.

Explanation:

Step1: Recall the section - formula on number line

Let the coordinate of \(B=- 5\) and the coordinate of \(F = 5\). Let the coordinate of \(X\) be \(x\). The ratio \(BX:XF = 3:2\). The formula for dividing a line - segment with endpoints \(a\) and \(b\) in the ratio \(m:n\) is \(x=\frac{ma+nb}{m + n}\). Here \(a=-5\), \(b = 5\), \(m = 3\), and \(n = 2\).

Step2: Substitute values into the formula

\[x=\frac{3\times(-5)+2\times5}{3 + 2}=\frac{-15 + 10}{5}=\frac{-5}{5}=-1\]

Answer:

\(-1\)