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

1 Answer
Alan P.
Dec 26, 2016

#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)#

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