Question 357239
{{{drawing(300,300,-5,5,-5,5,grid(1),graph(300,300,-5,5,-5,5,3x,3x+10))}}}
Find the perpendicular line that goes through (0,0).
Since perpendicular lines have slopes that are negative reciprocals,
{{{3*m2=-1}}}
{{{m2=-1/3}}}
{{{y=-(1/3)x+b}}}
Using the origin,
{{{0=-(1/3)(0)+b}}}
{{{b=0}}}
{{{y=-(1/3)x}}}
Now look for the intersection of {{{y=3x+10}}} and {{{y=-(1/3)x}}}
{{{-(1/3)x=3x+10}}}
{{{-x=9x+30}}}
{{{-10x=30}}}
{{{x=-3}}}
Then find the y coordinate,
{{{y=(1/3)(3)=1}}}
Now find the distance from (0,0) to (-3,1) using the distance formula,
{{{D^2=(x[2]-x[1])^2+(y[2]-y[1])^2}}}
{{{D^2=(-3-0)^2+(1-0)^2}}}
{{{D^2=9+1}}}
{{{highlight(D=sqrt(10))}}}
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{{{drawing(300,300,-5,5,-5,5,circle(-3,1,0.3),circle(0,0,0.3),grid(1),graph(300,300,-5,5,-5,5,3x,3x+10,-(1/3)x))}}}