Question

refer to the number line. find the coordinate of q on (overline{fl}) such that the ratio of fq to ql is 12:7. get a hint need help with this question?

Explanation:

Step1: Identify the coordinates of F and L

The coordinate of F is - 15 and the coordinate of L is 5.

Step2: Use the section - formula for a one - dimensional line

Let the coordinate of Q be \(x\). The ratio of \(FQ\) to \(QL\) is \(12:7\). The formula for finding the coordinate of a point \(Q\) that divides the line segment joining \(F(x_1)\) and \(L(x_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\). Here, \(x_1=-15\), \(x_2 = 5\), \(m = 12\), and \(n = 7\).

Step3: Substitute the values into the formula

\[

$$\begin{align*} x&=\frac{12\times5+7\times(-15)}{12 + 7}\\ &=\frac{60-105}{19}\\ &=\frac{- 45}{19}\\ &=- \frac{45}{19}\approx - 2.37 \end{align*}$$

\]

Answer:

\(-\frac{45}{19}\)