Question

Find the distance between the points given.
(2, 2) and (5,5)
3
O 32
o 72

Answer 1

`d = 3√(2)`

Step-by-step explanation:

The distance between two distinct points on the same plane (
`d`) can be calculated by the General Equation of the Line Segment, a derivation from the Pythagorean Theorem:

`d = \sqrt{(x_(B)-x_(A))^(2)+(y_(B)-y_(A))^(2)}` (1)

Where:

`(x_(A), y_(A))` - Initial point.

`(x_(B), y_(B))` - Final point.

If we know that
`(x_(A), y_(A)) = (2, 2)` and
`(x_B, y_B) = (5, 5)`, then the distance of the line segment is:

`d =\sqrt{(5-2)^(2)+(5-2)^(2)}`

`d = √(18)`

`d = 3√(2)`