The formula of a distance between a point (a, b)
and a line Ax + By + C = 0:
[tex]d=\dfrac{|Aa+Bb+C|}{\sqrt{A^2+B^2}}[/tex]
We have the point (6, -2) → a = 6, b = -2
and the line y = 2x - 4 → 2x - y - 4 = 0 → A = 2, B = -1, C = -4.
Substitute:
[tex]d=\dfrac{|(2)(6)+(-1)(-2)+(-4)|}{\sqrt{2^2+(-1)^2}}=\dfrac{|12+2-4|}{\sqrt{4+1}}=\dfrac{|10|}{\sqrt5}=\dfrac{10\sqrt5}{\sqrt5\cdot\sqrt5}\\\\=\dfrac{10\sqrt5}{5}=2\sqrt5[/tex]
Answer: d = 2√5
