# Let #l# be a line described by equation ax+by+c=0 and let #P(x,y)# be a point not on #l#. Express the distance, #d# between #l and P# in terms of the coefficients #a, b and c# of the equation of line?

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The distance ( d ) between the line ( l ) described by the equation ( ax + by + c = 0 ) and a point ( P(x, y) ) not on ( l ) can be expressed using the formula:

[ d = \frac{|ax + by + c|}{\sqrt{a^2 + b^2}} ]

Where:

- ( a ), ( b ), and ( c ) are the coefficients of the equation of the line ( l ).
- ( x ) and ( y ) are the coordinates of the point ( P(x, y) ).
- ( |ax + by + c| ) represents the absolute value of the expression ( ax + by + c ).
- ( \sqrt{a^2 + b^2} ) is the square root of the sum of squares of the coefficients ( a ) and ( b ).

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The distance (d) between a line described by the equation (ax + by + c = 0) and a point (P(x, y)) not on the line can be expressed as:

[ d = \frac{|ax + by + c|}{\sqrt{a^2 + b^2}} ]

So, the distance (d) is given by the absolute value of the expression (ax + by + c) divided by the square root of the sum of the squares of coefficients (a) and (b).

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