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An equation of a line and the coordinates of a point?

how can i find the perpendicular distance of the point from the given line...?? lets suuppose that the given point is (-a,-a) and the given equation of line is 3x-4y+8=0.... plz give the steps...

2 Answers

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  • 1 decade ago
    Favorite Answer

    first satisfy the given equation within the mod..... then divide by the square root of the sum of the squares of coefficients of x and y

    [] : mod

    d : perpendicular distance

    then

    d = [ Ax + By + C ] / ( A^2 + B^2 )^1/2

    for this question ,

    x = -a , y= -a A = 3 , B = -4 , C = 8

    therefore substitute the values

    d = [ 3 (-a ) + (-4)(-a) + 8 ] / ( 3^2 + ( -4 )^2 )^1/2

    d= [ -3a + 4a + 8 ] / 5

    d= [a + 8 ] / 5

    it is the answer ....... substitute the x if the answer ( a +8 ) is less than 0 then put it as positive because [ - k ] = k

    hope this helps..........

  • 1 decade ago

    perpendicular distance of Point (a,b) from the line lx + my + c =0 is given by the formula ;;;

    L = (al +bm +c ) /root( l^2 +m^2) therefore in the give equation

    L = ( --3 a---4a +8) / root (3^2 +4^2) or length = (--7a +8)/5 ans

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