Question

find the distance from (2,-7) to the line defined buy y==2x-6. express as a radical or a number rounded to the nearest hundredth

Answer 1

\[\sqrt((x-2)^2 + (y-(-7))^2) \]
y = 2x-6
\[\sqrt((x-2)^2+(2x+1)^2)\]
\[(x-2)^2 = x^2-4x+4; (2x+1)^2 = 4x^2+4x+1\]
Those two added gives.
\[5x^2+5\]
So our distance formula is this.
\[d=\sqrt(5x^2+5)\]
Find the minimum distance by taking the derivative and setting it equal to 0.
\[\frac{ 10x }{ 2\sqrt(5x^2+5) }=0\]
x = 0
Plug x = 0 in the distance formula that we got.
\[d=\sqrt(5)\]