Question

If x is a positive integer such that the distance between points P (x, 2) and Q (3, −6) is 10 units, then x =

Options

• 3

• -3

• 9

• -9

Answer 1

It is given that distance between P (x, 2) and Q(3 , - 6 )  is 10.

In general, the distance between A(x₁ , y ₁ )   and B (x₂ , y₂) is given by,

`AB^2 = ( x_2-x_1)^2 + (y_2 - y_1)^2`

So,

`10^2 = (x - 3)^2 + (2 + 6)^2`

On further simplification,

`(x - 3)^2 = 36 `

            ` x = 3 +- 6`

              `= 9 - 3`

We will neglect the negative value. So,

x = 9