Question

How do you find the distance between (3,2) and (1,-1)?

Answer 1

Distance between `(3,2)` and `(1,-1)` is`sqrt(13)`

Explanation:

(see image below)

The horizontal distance between `(1,-1)` and `(3,2)` is
`color(white)("XXX")Delta x = abs(3-1) = 2`

The vertical distance between `(-1,-1)` and `(3,2)` is
`color(white)("XXX")Delta y = abs((-1)-2) = 3`

By the Pythagorean Theorem the distance between `(-1,1)` and `(3,2)` is
`color(white)("XXX")sqrt((Delta x)^2+(Delta y)^2)`

`color(white)("XXX")= sqrt(2^2+3^2)`

`color(white)("XXX")= sqrt(13)`