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Line ℓ has equation y=–x–3. Find the distance between ℓ and the point G(7,–6).

 Sep 21, 2020
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There IS a formula for point to line distance...but I am not going to use it

slope of given line is -1    perpindicular is  -  1 / -1  = 1

point slope form going thru 7,-6   and perpindicular

 y+6 = 1 (x-7)     or    y = x-13

 

the intersection of these two lines is   found:     x - 13 = -x -3     so x = 5      then y = -8

Now distance between   7, -6    and    5, -8

        (7-5)^2  + (-6- -8)^2 = d^2

d = sqrt 8 = 2 sqrt2

 Sep 21, 2020

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