Question

refer to the number line. find the coordinate of q on fl such that the ratio of fq to ql is 12:7.

Explanation:

Step1: Determine 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

If a point Q divides the line segment joining \(x_1\) and \(x_2\) in the ratio \(m:n\), the coordinate of Q is given by \(x=\frac{mx_2+nx_1}{m + n}\). Here, \(x_1=-15\), \(x_2 = 5\), \(m = 12\), and \(n = 7\).
\[x=\frac{12\times5+7\times(-15)}{12 + 7}\]

Step3: Simplify the expression

First, calculate the numerator: \(12\times5+7\times(-15)=60-105=-45\). Then, the denominator is \(12 + 7=19\). So, \(x =-\frac{45}{19}\approx - 2.37\).

Answer:

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