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Given A is (2,1),B is (3,2) and P is(x,y).if PA=PB show x+y=4. ?

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given A is (2,1),B is (3,2) and P is(x,y).if PA=PB show x+y=4. tq.

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  1. Here is the equation for the length of line PA in terms of x and y:

    PA=sqrt((x-2)^2+(y-1)^2) (pythagorean theorem)

    Here is the equation for the length of line PB in terms of x and y:

    PB=sqrt((x-3)^2+(y-2)^2)

    We know PA=PB, so:

    sqrt((x-2)^2+(y-1)^2)=sqrt((x-3)^2+(y-...

    Now we simplify the equation.

    First, square both sides to get rid of the sqrt():

    (x-2)^2+(y-1)^2=(x-3)^2+(y-2)^2

    Expand everything:

    x^2-4x+4+y^2-2y+1=x^2-6x+9+y^2-4y+4

    Subtract x^2 and y^2 from both sides:

    -4x+4-2y+1=-6x+9-4y+4

    -4x-2y+5=-6x-4y+13

    Add 2y to both sides

    -4x+5=-6x-2y+13

    Add 4x to both sides

    5=-2x-2y+13

    Subtract 13 from both sides:

    -8=-2x-2y

    Divide both sides by -2:

    4=x+y

    Therefore, x+y=4


  2. (x-2)^2+(y-1)^2 = (x-3)^2 + (y-2)^2

    x^2 -4x +4 +y^2-2y+1 = x^2-6x+9 +y^2-4y+4

    -4x -2y+1 = -6x-4y+9

    2x+2y = 8

    x+y = 4


  3. Using Distance Formula & Equating ...PA + PB, we get

    (x-2)^2+(y-1)^2 = (x-3)^2+(y-2)^2      (Cancelling the roots from both sides)

    Open the brackets ...& Solve. Weget

    2x+2y=8

    Therfore, x+y=4.

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