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

1 Answer
Jul 7, 2016

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#