Question

Find the coordinate of the indicated point on a number line. Five-sixths of the distance from 1 to −13

Answer 1

Answer: The coordinate is
`-10(2)/(3)` or about -10.67

Explanation:

First, determine the distance from 1 to -13 on the number line:

`d = |x_1-x_2|=|1-(-13)|=14`

Next step is calculating Five-sixths of this distance:

`(5)/(6)d=(5)/(6)\cdot14=(35)/(3)=11(2)/(3)`

Finally, we "walk" that frcation of distance in the direction from 1 toward -13 (i.e., in the negative direction). The new coordinate x* is:

`x^*=1-11(2)/(3)=-10(2)/(3)=-10.\overline{6}`