Hey,(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: The scalar product

**Physics Forums | Science Articles, Homework Help, Discussion**