Question

it says i need to find the shortest distance between the point and the line for geometry honors, how would i figure it out

Answer 1

The given line equation is,

`3x-y=-6`

The given point is ,

`(5,1)`

The graph will look like this,

let us rewrite the line equtaion as ,

`3x-y+6=0`

now, let us compare with the general equation of line,

`Ax+By+C=0`

then, A= 3,B=-1 and c= 6.

let us use the formula,

`\begin{gathered} d=\fracAx+By+c{\sqrt[]{A^2+B^2}} \\ d=\frac3*5+(-1)*1+6{\sqrt[\square]{3^2+(-1)^2}} \\ d=\frac15-1+6{\sqrt[\square]{9+1}} \\ d=\frac{20}{\sqrt[\square]{10}} \\ d=6.32 \end{gathered}`

The shortest distance is 6.32 .