 Hello and welcome to the session. The given question says if the point Pxy is equidistant from the points A and B proves that 3x is equal to 2y. Let's start with a solution. Here we are given that the point P with coordinates x, y is equidistant from the points A with coordinates 5, 1 and B with coordinates minus 1 and 5. So this implies that Ap is equal to Bp. First we just learn the distance formula with the help of which we shall be finding Ap and Bp. That says for any 2 points A and B with coordinates x1, y1 and x2, y2 the distance between them is equal to the square root of x2 minus x1 whole square plus y2 minus y1 whole square. So here we have Ap as square root of 5 minus x whole square plus 1 minus y whole square is equal to square root of minus 1 minus x whole square plus 5 minus y whole square. Now on squaring both the sides we have on the left hand side 5 minus x whole square plus 1 minus y whole square is equal to minus 1 minus x whole square plus 5 minus y whole square. Now simplifying it further here we have 25 minus 10x plus x square plus 1 minus 2y plus y square is equal to 1 plus x square plus 2x plus 25 minus 10y plus y square. Now here y square cancels out with y square, x square with x square and now we have 25 plus 1 gives 26 minus 10x minus 2y is equal to on the right hand side we have 2x minus 10y plus 26 or this is further equal to taking all the variables on one side we have minus 10x minus 2x is equal to minus 10y plus 2y plus 26 minus 26 or this is further equal to minus 12x is equal to minus 8y 26 cancels out with minus 26 or we have now minus 4 is common on both the sides therefore dividing both the sides by minus 4 here we have 3x and here we have 2y which we get on dividing both sides by minus 4 hence we have 3x is equal to 2y so this completes the session buy and take care.