Question

Find the point which is equidistant from the points (3,2) and (7,2)​

Answer 1

Solution :-

We have to find the point which is equidistant from (3, 2) and (7,2)

Let the point P is equidistant from (3,2) and (7,2)

The co-ordinates of point P = (x,y)

Since they are equidistant Their distances also equal

So,

PA = PB

PA = Distance between P and A

PB = Distance between P and B

Distance formula :-

$\sqrt{(x_1-x_2)^2 +(y_1-y_2)^2}$

$PA \: = \sqrt{(x - 3) {}^{2} + (y - 2) {}^{2} }$

$PB \: = \sqrt{(x - 7) {}^{2} + (y - 2) {}^{2} }$

$PA {}^{2} = (x - 3) {}^{2} + (y - 2) {}^{2}$

$PB {}^{2} = (x - 7) {}^{2} + (y - 2) {}^{2}$

$PA {}^{2} = PB {}^{2}$

$(x - 3) {}^{2} + (y - 2) {}^{2} = ( x- 7) {}^{2} + (y - 2) {}^{2}$

$(x - 3) {}^{2} = (x - 7) {}^{2}$

$x {}^{2} - 6x + 9 = x {}^{2} - 14x + 49$

$- 6x + 9 = - 14x + 49$

$- 6x + 14x + 9 - 49 = 0$

$8x -40 = 0$

$8x = 40$

$x = 5$

Any point on x = 5 will be the answer.

Answer is : x = 5... Which is a line, No specific point is obtained that any point of y coordinate on line x = 5 will be the answer be it (5,0,),(5,1),(5,2),(5,3),...