Question

What is the length of the segment with endpoints `(0,-1)` and `(4, 7)`?

Answer 1

Length from (0,-1) to (4,7): `color(blue)(4sqrt(5))`

Explanation:

The horizontal distance, `Deltax`, between `(0,-1)` and `(4,7)` is `abs(4-0)=4`
The vertical distance, `Deltay`, between `(0,-1)` and `(4,7)` is `abs(7-(-1))=8`

Based on the Pythagorean Theorem the distance between the two points is
`color(white)("XXX")sqrt(4^2+8^2)=sqrt(4^2 * (1+2^2))=4sqrt(5)`