# Rotate These Straight Lines!

Geometry Level 3

The line $$\mathbb{L}$$ has intercepts $$a$$ and $$b$$ on the coordinate axes. When keeping origin fix ,the coordinate axes are rotated through a fixed angle then the same line has intercepts $$p$$ and $$q$$ on the rotated axes. Then which option is correct?

$$\LARGE A)$$: $$\frac {1}{a^2} + \frac {1}{b^2} = \frac {1}{p^2} + \frac {1}{q^2}$$

$$\LARGE B)$$: $$\frac {1}{a^2} + \frac {1}{p^2} = \frac {1}{b^2} + \frac {1}{q^2}$$

$$\LARGE C)$$: $$a^2 + p^2 = b^2 + q^2$$

$$\LARGE D)$$: $$a^2 + b^2 = p^2 + q^2$$

Details and Assumptions:

• The value $$\arctan \left ( \frac {3}{4} \right )$$ is not used, it's just for illustration purpose.

Picture Source File: Wikimedia Rotate File

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