Question

refer to the number line. find the coordinate of point x such that the ratio of fx to xd is 5:3.

Explanation:

Step1: Identify the coordinates of F and D

The coordinate of $F$ is $5$ and the coordinate of $D$ is $1$.

Step2: Use the section - formula for a number line

The formula to find the coordinate of a point $X$ that divides the line - segment joining points $x_1$ and $x_2$ in the ratio $m:n$ is $x=\frac{mx_2+nx_1}{m + n}$. Here, $x_1 = 1$ (coordinate of $D$), $x_2 = 5$ (coordinate of $F$), $m = 5$, and $n = 3$.
\[x=\frac{5\times1+3\times5}{5 + 3}\]

Step3: Simplify the expression

First, calculate the numerator: $5\times1+3\times5=5 + 15=20$. Then, divide by the denominator: $\frac{20}{8}=2.5$.

Answer:

$2.5$