Suppose that $$A1$$,$$2$$ and $$B3$$,$$4$$ be two points and P be a point on $$y=x$$ such that $$PA+PB$$ is minimum then the point P

Question

Suppose that $$A1$$,$$2$$ and $$B3$$,$$4$$ be two points and P be a point on  $$y=x$$  such that $$PA+PB$$ is minimum then the point P

Infinity Learn · Accepted Answer

Suppose that the images of  $$A1$$,$$2$$ and $$B3$$,$$4$$  in the line $$x=y$$ are  C  and D respectively. The point P  is the point of intersection of the lines AD  and $$x=y$$  , it is coincide with the point of intersection of the lines BC  and   $$x=yThe$$ image of $$B3$$,$$4$$ in the line $$y=x$$  is $$D4$$,$$3$$   The equation of the line joining $$D4$$,$$3$$ an $$A1$$,$$2$$ is   y−$$2=2$$−$$31$$−$$4x$$−$$1This$$ can be simplified as y−$$2=13x$$−$$13y$$−$$6=x$$−$$1x$$−$$3y+5=0Plug$$ in $$x=y$$ to get the point of intersection of the above line and the line $$x=y$$. It implies thatx−$$3x+5=02x=5x=52Therefore$$, $$P=52$$,$$52$$

Suppose that $A (1, 2)$ and $B (3, 4)$ be two points and P be a point on y=x such that $|PA + PB|$ is minimum then the point P

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Suppose that A1,2 and B3,4 be two points and P be a point on y=x such that PA+PB is minimum then the point P

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Suppose that $A (1, 2)$ and $B (3, 4)$ be two points and P be a point on y=x such that $|PA + PB|$ is minimum then the point P