Line ℓ has equation y=–x–3. Find the distance between ℓ and the point G(7,–6).
+37159 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
