Question

What is the distance between the points (21,-30) and (3, 8)?

Answer 1

42.0

Explanation:

First, calculate the horizontal distance and vertical distance between the points. To do this we use the `x` and `y` values of the co-ordinates.
The horizontal distance, `a`:
`a=x_1-x_2=21-3=18`
The vertical distance, `b`
`b=y_1-y_2=-30-8=-38`
These two distances can be considered as the base and vertical side of a right angled triangle, with the distance between the two as the hypotenuse.
The we use Pythagoras' theorem to find the hypotenuse, `c`.
`c^2=a^2+b^2`
`c^2=(18)^2+(-38)^2`
`c^2=1768`

`c=sqrt(1768)=42.0 ("3 s.f.")`
The distance between the points is then `42.0`