Question

an ant is on top of a tree 23 meters tall, directly above her home, which is 0.3 meters below the ground. which 2 of the following expressions represents the distance between the ant and her home? choose 2 answers: a $|23 + 0.3|$ b $|0.3 - 23|$ c $|-0.3 - 23|$

Explanation:

Step1: Define positions

Let the ground - level be 0. The ant's position is at 23 meters (above ground) and the home's position is at - 0.3 meters (below ground).

Step2: Use distance formula

The distance \(d\) between two points \(x_1\) and \(x_2\) is \(d=\vert x_1 - x_2\vert\). Here, if \(x_1 = 23\) and \(x_2=-0.3\), then \(d=\vert23-(- 0.3)\vert=\vert23 + 0.3\vert\). Also, if \(x_1=-0.3\) and \(x_2 = 23\), then \(d=\vert-0.3 - 23\vert\).

Answer:

A. \(\vert23 + 0.3\vert\)
C. \(\vert-0.3 - 23\vert\)