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Today I was given a problem to solve in class and was told to complete it for homework. This problem is as follows:

The line y=mx + c has a gradient m and cuts the y axis at (0,c). Thus we can write the parametric vector equation of the line as:

[tex]r = cj +\lambda (i + mj)[/tex]

Using this fact show that that the perpendicular distance from point [tex]A(x_1 , y_1)[/tex] to y = mx + c is:

[tex]\mid(\frac{mx_{1} - y_{1} + c}{\sqrt{m^2 + 1}})\mid[/tex]

If y = mx + c is instead written as ax + by + d = 0 show that the perpendicular distance of point [tex]A(x_1 , y_1)[/tex] to as ax + by + d = 0 is given by:

[tex]\mid(\frac{ax_{1} - by_{1} + d}{\sqrt{a^2 + b^2}})\mid[/tex]

This diagram which I drew to help me may help:

______________________

I have tried solving this problem by using vectors:

and I know that the dot product of [tex]( x_1 , y_1 )[/tex] and y = mx + c is equal to zero but from there onwards I am not sure on how to approach this problem. All help is appreciated,

thanks, Pavadrin

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# The scalar product

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