Question

If the points P (x, y) is equidistant from A (5, 1) and B (−1, 5), then

Options

•  5x = y

• x = 5y

• 3x = 2y

• 2x = 3y

Answer 1

It is given that P (x , y)   is equidistant to the point `A (5,1) " and " B (-1 , 5)`

So,

`PA^2 = PB^2`

So apply distance formula to get the co-ordinates of the unknown value as,

`(x - 5)^2 + (y - 1)^2 = (x +1)^2 + (y-5)^2`

On further simplification we get,

25-10x + 1 - 2y = 1 +2x + 25 - 10y

So,

12x = 8y

Thus,

3x = 2y