A ray of light is sent along the line which passes through the point (2$$, $$3). The ray is reflected from the point P on $$x-axis$$. If the reflected ray passes through the point (6$$, $$4), then the coordinates of P are

Question

Infinity Learn · Accepted Answer

Let P≡α,$$0$$. Let the reflected ray makes an angle θ with $$+ve$$ direction of $$x-axis$$, then the incident ray makes angle π$$-$$θ with positive direction of $$x-axis$$. The slope of the incident ray $$is=0-3$$α$$-2=$$$$tan$$π$$-$$θ i.e., $$tan$$θ$$=3$$α$$-2The$$ slope of the reflected ray $$is=4-06-$$α$$=$$$$tan$$θ i.e., $$tan$$θ$$=46-$$αFrom Eq. (1) and (2), we $$get3$$α$$-2=46-$$α⇒$$18-3$$α$$=4$$α$$-8$$⇒$$7$$α$$=26$$  or  α$$=267$$∴The coordiantes of A are $$267$$,$$0$$

A ray of light is sent along the line which passes through the point (2, 3). The ray is reflected from the point P on x-axis. If the reflected ray passes through the point (6, 4), then the coordinates of P are

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material