Question

Two ants start at the origin of the rectangular grid shown above where each unit represents an inch. They roam around in different directions for exactly 30 seconds. Ant A ends at point (-3,5) while Ant B ends at points (4,-2). How far apart are the two ants at the end of 30 seconds?

Answer 1

To help clarify the problem, we can plot the two ants on a graph (see attached image). However, we don't need the graph to solve the problem.

Let's first find the distance in their 'x' values:
= |-3| + |4|
The '| |' means that we don't care if it is negative, we just want the positive value.
= |-3| + |4| is the same thing as = 3 + 4
= 7

Now let's find the distance in their 'y' values:
= |5| + |-2|
= 7

From here, since we have the 'x' and 'y' distances, we can create a triangle. The 'x' and 'y' will be our side lengths, and the hypotenuse is then the distance between the two ants. 

In order to find the hypotenuse, we use the Pythagorean theorm: $c^{2}=a^{2}+b^{2}$

Now we plug and solve:
$c^{2}=(7)^{2} + (7)^{2}$
$c^{2}=98$
$c= \sqrt{98}$

∴The distance between the two ants is $\sqrt{98}$ or 9.899

Hope this helps!