Geo2.19

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Show that the equation of the straight line passing through (x_{1},y_{1})\, and making an angle of \theta \, with the X-axis in positive direction is {\frac  {x-x_{1}}{\cos \theta }}={\frac  {y-y_{1}}{\sin \theta }}\,.

As the straight line makes an angle 'theta' with X-axis,the slope of the line is

m=\tan \theta \, since the slope is defined by {\frac  {y_{2}-y_{1}}{x_{2}-x_{1}}} and this also gives {\frac  {opp}{adj}}, i.e. \tan \theta \,

Therefore the equation of the straight line is

y-y_{1}=\tan \theta (x-x_{1})\,

that is

y-y_{1}={\frac  {\sin \theta }{\cos \theta }}(x-x_{1})\,

Rearranging the variables,we get

{\frac  {x-x_{1}}{\cos \theta }}={\frac  {y-y_{1}}{\sin \theta }}\,


Main Page:Geometry:Straight Lines-I