A ray of light travels along the line $$2x$$−$$3y+5=0$$ and strikes a plane mirror lying along the line $$x+y=2$$ The equation of the straight line containing the reflected ray is

Question

A ray of light travels along the line $$2x$$−$$3y+5=0$$  and strikes a plane mirror lying along the line $$x+y=2$$ The equation of the straight line containing the reflected ray is

Infinity Learn · Accepted Answer

Let θ  be the angle which the ray  $$2x$$−$$3y+5$$ ⊨$$0makes$$ with the line $$x+y=2$$  then  ⁡θ$$=2/3+11$$−$$2/3(1)$$ $$=$$|$$5$$|$$=5$$  Reffected ray makes angle −θ  with $$x+y=2$$ so if the slopeof the reflected ray is m then $$m+11$$−$$m=$$$$tan$$⁡$$($$−θ$$)=$$−$$5$$               ⇒ $$m=3/2$$. Also, the reflected ray passes through  (1/5$$,$$9/5) the point of intersection of the ray and the lineHence equation of the reflected ray $$is(y$$−$$9/5)=3/2(x$$−$$1/5)$$⇒$$3x$$−$$2y+3=0$$

Equation of line in Straight lines

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A ray of light travels along the line $2 x - 3 y + 5 = 0$ and strikes a plane mirror lying along the line $x + y = 2$ The equation of the straight line containing the reflected ray is

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Equation of line in Straight lines

Remember concepts with our Masterclasses.

A ray of light travels along the line 2x−3y+5=0 and strikes a plane mirror lying along the line x+y=2 The equation of the straight line containing the reflected ray is

Ready to Test Your Skills?

free study material

A ray of light travels along the line $2 x - 3 y + 5 = 0$ and strikes a plane mirror lying along the line $x + y = 2$ The equation of the straight line containing the reflected ray is