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# What integer represents the distance the snail traveled from its original position?

A snail climbs 3 inches then slides 6 inches. What integer represents the distance the snail traveled from its original position?

### 1 Answer by Expert Tutors

Andrew K. | Expert Math and Physics Tutor - Many successful students!Expert Math and Physics Tutor - Many suc...
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Hi Alicia - I think that your word problem may suffer from poor wording.

DISTANCE deals with the actual path taken - direction does not matter. For example, if you drive your car 3 miles north, then 6 miles east, you have driven a total DISTANCE of 9 miles.  By the wording of the problem given, the answer should be 9 inches.

However, if we are concerned with calculating DISPLACEMENT, we are only concerned with the overall change in position from start to finish.

In this case, we want to construct a triangle showing the path taken, and calculate the distance between the start and end points.

_ _ _6_ _ _
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3|
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For a right triangle, we can calculate the "displacement" (hypotenuse) using the Pythagorean Theorem: a2 + b2 = c2

So the overall displacement (hypotenuse) = √(32+62)

Displacement = √(45)

= √(9) * √(5)

= 3 √(5)