Question

example 1 locate a point at a fractional distance
find b on $overline{ac}$ that is $\frac{1}{4}$ of the distance from a to c.

Explanation:

Step1: Find the distance between A and C

The coordinate of A is - 5 and the coordinate of C is 7. The distance formula for two points on a number - line is \(d=\vert x_2 - x_1\vert\). So, \(d=\vert7-( - 5)\vert=\vert7 + 5\vert = 12\).

Step2: Calculate one - fourth of the distance

We want to find a point B that is \(\frac{1}{4}\) of the way from A to C. One - fourth of the distance \(d\) is \(\frac{1}{4}\times12 = 3\).

Step3: Find the coordinate of B

To find the coordinate of B, we start at the coordinate of A and move \(\frac{1}{4}\) of the distance towards C. The coordinate of B is \(-5+3=-2\).

Answer:

The coordinate of point B is - 2.