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Calculus

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Find the point on the line -3 x + y + 4 =0 which is closest to the point ( -5, 0 ).

  • Calculus - ,

    distance=sqrt((x+5)^2+ (y)^2)

    but y=3x-4
    distance= sqrt((x+5)^2 + (3x-4)^2)

    I think it will be easier to do this..
    distance^2=((x+5)^2+(3x-4)^2) then take the deravative

    2distane*ddistan/dx=0=2(x+5)+2(3x-4)*3

    or x+5=-9x+12 check that, then solve for x, then solve for y on the line

    check my work, I did it all in my head and on the keyboard.

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