Find the distance between the points (¼ , ½) and (5, 6) ???

1 Answer
Dean R.
Jun 25, 2018

distance #d = \sqrt{(5-1/4)^2+(6-1/2)^2} = {13 sqrt{5}}/4#

Explanation:

When we have a Cartesian plane, there's an easy right triangle between any two points #(a,b)# and #(c,d)#. One leg goes parallel to the #x# axis, length #|c-a|# and the other parallel to the #y# axis, length #|d-b|.# So the distance #d# between the points satisfies

#d^2 = (c-a)^2 + (b-d)^2#

We apply that here and get

#d^2 = (5-1/4)^2+(6-1/2)^2 = (19/4)^2+(11/2)^2=845/16#

#d = sqrt{845}/4 = {13 sqrt{5}}/4#

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