SOLUTION: On his way to room, Liza traveled 3 km North and 4 km West. What is the displacement made by Liza?

Question 1196022: On his way to room, Liza traveled 3 km North and
4 km West. What is the displacement made by Liza?

Found 3 solutions by math_tutor2020, Alan3354, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Define these points
A = Liza's starting point
B = the point 3 km directly north of point A
C = the point 4 km directly west of point B, which is Liza's ending point

The points form a right triangle. The 90 degree angle is at point B.
I recommend drawing out a quick sketch of this. It doesn't need to be perfect or to scale.
See the diagram at the bottom.

We can use the pythagorean theorem to find the distance from A (Liza's starting point) to C (Liza's ending point).
All displacement cares about are these two points. Any stuff in the middle is ignored.
Think of displacement being the ultimate shortcut you can take when going from the beginning directly to the ending.

The right triangle has legs of a = 3 and b = 4
The unknown hypotenuse is c

Let's apply the pythagorean theorem to solve for c.

We have a 3-4-5 right triangle, which is perhaps the most famous of the many pythagorean triples.
To confirm this is correct, you could use a tool like GeoGebra as shown below

Therefore, the distance from A to C is 5 km.
This is the displacement.

Answer: 5 km

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!

Answer by ikleyn(52873)   (Show Source): You can put this solution on YOUR website!
.
On his way to room, Liza traveled 3 km North and
4 km West. What is the displacement made by Liza?
~~~~~~~~~~~~~~~~~~

On " his " or " her " way ?

Lowest possible score to the person who composed this problem.

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