A ray of light passing through the point (3$$, $$7) reflects on the $$x-axis$$ at a point A and the reflected ray passes through the point (2$$, $$5), the coordinates of A are

Question

A ray of light passing through the point (3$$, $$7) reflects on the $$x-axis$$ at a point A and the reflected ray passes through the point (2$$, $$5), the coordinates of A are

Infinity Learn · Accepted Answer

Let p be the given point (3$$, $$7) and the coordinates of A be (x$$, $$0) so, if the ray PA makes an angle θ with the positive direction of $$x-axis$$, the reflected ray AQ , where Q is (2$$, $$5), will make the same angle q with the negative direction of $$x-axis$$. So the slope of PA $$=$$ – (the$$ slope of $$QA)⇒ $$73$$−$$x=$$−$$52$$−x⇒ $$7(2$$−$$x)+5(3$$−$$x)=0$$⇒ $$x=2912$$⇒    coordinates of A are $$2912$$,$$0$$.

A ray of light passing through the point $(3, 7)$ reflects on the $x -$ axis at a point A and the reflected ray passes through the point $(2, 5)$ , the coordinates of $A$ are

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A ray of light passing through the point (3, 7) reflects on the x-axis at a point A and the reflected ray passes through the point (2, 5), the coordinates of A are

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A ray of light passing through the point $(3, 7)$ reflects on the $x -$ axis at a point A and the reflected ray passes through the point $(2, 5)$ , the coordinates of $A$ are