Question

The horizontal distance between two points.

Answer 1

The horizontal distance between two points, also known as the displacement or range, is the straight line distance an object moves between its initial and final positions.

Step-by-step explanation:

The horizontal distance between two points, also known as the displacement or range, is the straight line distance an object moves between its initial and final positions.

Displacement is a vector quantity and has both magnitude and direction, while distance traveled is a scalar quantity and only has magnitude.

For example, if an object moves 5 meters to the right and then 3 meters to the left, its displacement is 2 meters to the right, but the distance traveled is 8 meters.

Answer 2

We use the Pythagoras Theorem to derive a formula for finding the distance between two points in 2- and 3- dimensional space.

Let

P = (x 1, y 1)

Q = (x 2, y 2)

be two points on the Cartesian plane

Then from the Pythagoras Theorem we find that the distance between P and Q is

PQ=((x2-x1)^2+(y2-y1)^2)^0.5

In a similar way

it can be proved that if

P = (x 1, y 1, z1) and

Q = (x 2, y 2, z2) are two points in the 3-dimensional space,

the distance between P and Q is

PQ=((x2-x1)^2+(y2-y1)^2+(z2-z1)^2)^0.5