Question

refer to the number line. find the coordinate of point x on $overline{af}$ that is $\frac{1}{3}$ of the distance from a to f.

Explanation:

Step1: Find the coordinates of A and F

The coordinate of A is - 5 and the coordinate of F is 4.

Step2: Calculate the distance between A and F

The distance formula on a number - line is \(d=\vert x_2 - x_1\vert\). Here, \(x_1=-5\) and \(x_2 = 4\), so \(d=\vert4-(-5)\vert=\vert4 + 5\vert=9\).

Step3: Find the position of point X

If point X is \(\frac{1}{3}\) of the distance from A to F, we first find the distance from A to X. Let the coordinate of X be \(x\). The distance from A to X is \(\frac{1}{3}\times9 = 3\). Then, using the formula for distance on a number - line \(\vert x-(-5)\vert=3\), which simplifies to \(x + 5=3\) (since we are moving from A towards F). Solving for \(x\), we get \(x=-2\).

Answer:

The coordinate of point X is - 2.