Question 1083157
A line has a y-intercept of 8 and an x-intercept of -12.
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{{{m=8/12=2/3}}};
{{{y=(2/3)x+8}}}------equation for the described given line



Line from the origin  (0,0), perpendicular to given line:
{{{y=-(3/2)x}}}



Their intersection
{{{(2/3)x+8=-(3/2)x}}}
{{{(2/3+3/2)x=-8}}}
{{{(4/6+9/6)x=-8}}}
{{{(13/6)x=-8}}}
{{{x=-8(6/13)}}}
{{{x=-48/13}}}
-
{{{y=-(3/2)(-48/13)}}}
{{{y=(3*48)/(2*13)}}}
{{{y=3*24/13}}}
{{{y=72/13}}}
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Distance from origin
{{{sqrt((48/13)^2+(72/13)^2)}}}


{{{(1/13)sqrt(48^2+72^2)}}}


{{{(1/13)sqrt(7488)}}}

{{{highlight((1/13)*24*sqrt(13))}}}







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7488
832*9
4*208*9
4*4*52*9
4*4*4*13*9