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 distance between A and F

The coordinate of A is - 5 and the coordinate of F is 4. The distance formula between two points \(x_1\) and \(x_2\) on a number - line is \(d=\vert x_2 - x_1\vert\). So, \(d=\vert4-(-5)\vert=\vert4 + 5\vert = 9\).

Step2: Calculate the distance from A to X

We want to find a point X on \(\overline{AF}\) such that the distance from A to X is \(\frac{1}{3}\) of the distance from A to F. So the distance from A to X is \(\frac{1}{3}\times9 = 3\).

Step3: Find the coordinate of X

Starting from A with coordinate - 5, if we move 3 units to the right (since we are moving from A to F which is in the positive direction), we use the formula \(x=-5 + 3\). So \(x=-2\).

Answer:

• 2