__Category__: Analytic Geometry"Published in Vacaville, California, USA"

Given the equation of a line

Find the new equation of a line if the given line is rotated about the origin at 45°.

__Solution__:

To illustrate the given problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life |

If the given equation is written in rectangular coordinate system, then we need to convert it into polar coordinate system as follows

Next, substitute θ with θ - 45° and then expand using the sum and difference of two angles formula, we have

Convert the above equation into rectangular coordinate system in order to get its final equation. Therefore, the new equation of a line is