Question

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

Answer 1

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`