# An ant crawls 4 cm south and then turns east and crawls 6 cm. What is the distance the ant crawled and what is its displacement?

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t-nez | Certified Educator

The ant crawled a distance of 10 cm. (4 cm +6 cm). Distance is how much ground the ant covered. It's a scalar quantity so it doesn't include direction.

Displacement is a vector quantity that refers to the ant's change in position. The ant's displacement is the distance between its starting and ending positions, regardless of the route that it took to get there. Since the ant made a 90 degree turn, you can use the Pythagorean Theorem to find the displacement:

`a^2 + b^2 = c^2`

Where c, the hypotenuse of the right triangle formed by the ant's path, represents the displacement because it's the shortest distance from where the ant started to where it ended.

`c =sqrt(a^2 + b^2) =sqrt(16 +36) = 7.2`

Displacement = 7.2 meters