Question

modeling real life the number line shows the temperatures at 2:00 a.m. and 2:00 p.m. in the gobi desert. find the distance between the points.
the distance between the two points is □
interpret the distance between the points.

Explanation:

Step1: Use the distance formula on the number line

The distance between two points \(a\) and \(b\) on a number line is \(|a - b|\). Here, \(a=-11\) and \(b = 38\).
So, the distance \(d=| - 11-38|\)

Step2: Simplify the expression

\(|-11 - 38|=|-49|\)
Since the absolute value of \(-49\) is \(49\) (because \(|x|=

$$\begin{cases}x, &x\geq0\\-x, &x < 0\end{cases}$$

\), and for \(x=-49\), \(| - 49|=-(-49)=49\))

Answer:

The distance between the two points is \(49\). This means the temperature difference between 2:00 A.M. and 2:00 P.M. in the Gobi Desert is \(49^{\circ}F\)