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

it says i need to find the shortest distance between the point and the line for geometry-example-1
User Kamalone
by
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1 Answer

3 votes

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 .

it says i need to find the shortest distance between the point and the line for geometry-example-1
User Suslik
by
8.1k points

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