# How can I calculate the magnitude of displacement?

May 29, 2018

$\text{Please study the animations and drawings carefully.}$

#### Explanation:

• think of a point P on the curvilinear path that moves from point A to point B.
• The movement of the P point can be described by a reference point.

• That reference point is O (0,0).

• The coordinates of points A and B are $\left({x}_{1} , {y}_{1}\right)$and $\left({x}_{2} , {y}_{2}\right)$ respectively.

• Now let's draw a vector pointing to the first position of the P point. This vector is the position vector.

• As the dot moves, the length and direction of the vector change.

• We describe the change in the position of the point P with a vector because the displacement takes place in a certain direction.

• This vector is represented by green color.

• the magnitude of the displacement vector (green) can be calculated by various methods.

• We can use the Pythagorean theorem in the ABC triangle.

• $| o | = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$