Suppose that $$A5$$,$$6and$$ $$B3$$,$$4$$ be two points and P be a point on $$x-$$ axis such that $$PA+PB$$ is minimum then the point P is

Question

Suppose that $$A5$$,$$6and$$ $$B3$$,$$4$$ be two points and P be a point on $$x-$$ axis such that $$PA+PB$$ is minimum then the point  P is

Infinity Learn · Accepted Answer

Suppose that the images of $$A(5$$,$$6)$$ and $$B(3$$,$$4)$$ in the $$x-axis$$ are C and D respectively.  The point P is the point of intersection of the lines AD and $$x-axis$$, it is coincide with the  point of intersection of the lines BC and $$x-axis$$  The image of $$B(3$$,$$4)$$ in the $$x-axis$$ is $$D(3$$,−$$4)$$ The equation of the line joining $$D(3$$,−$$4)$$ and $$A(5$$,$$6)$$ is y−$$6=6+45$$−$$3(x$$−$$5)This$$ can be simplified as y−$$6=6+45$$−$$3x$$−$$5y$$−$$6=5x$$−$$5y$$−$$6=5x$$−$$255x$$−y−$$19=0Plug$$ in  $$y=0$$ to get the point of intersection of the above line and  $$x-axis$$. It implies $$that5x=19x=195$$ Therefore, $$P=195$$,$$0$$

Suppose that $A (5, 6)$ and $B (3, 4)$ be two points and $P$ be a point on $x -$ axis such that $|P A + P B|$ is minimum then the point $P$ is

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Suppose that A5,6and B3,4 be two points and P be a point on x- axis such that PA+PB is minimum then the point P is

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Suppose that $A (5, 6)$ and $B (3, 4)$ be two points and $P$ be a point on $x -$ axis such that $|P A + P B|$ is minimum then the point $P$ is