Question

How do you find the distance between (-2,4), (5,8)?

Answer 1

`abs((-2,4):(5,8))=color(green)(sqrt(65))`

Explanation:

The horizontal distance (`Deltax`)between `(-2,4)` and `(5,8)` is the absolute value of the difference between the `x` components of the coordinates:
`color(white)("XXX")Deltax = abs(5-(-2))=7`

Similarly, the vertical distance (`Deltay`)between `(-2,4)` and `(5,8)` is the absolute value of the difference between the `y` components of the coordinates:
`color(white)("XXX")Deltax = abs(8-4)=4`

Using the Pythagorean Theorem the distance between `(-2,4)` and `(5,8)` is
`color(white)("XXX")d=sqrt(7^2+4^2)=sqrt(65)`