Question

The length of a line segment joining A (2, −3) and B is 10 units. If the abscissa of B is 10 units, then its ordinates can be

Options

• 3 or −9

• −3 or 9

• 6 or 27

• −6 or −27

Answer 1

It is given that distance between P (2,−3) and  Q ( 10 , y ) is 10.

In general, the distance between A`(x_1 ,y_1) " and " B (x_2 , y_2) ` is given by,

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

So,

`10^2 = (10 - 2)^2 +(y + 3)^2`

On further simplification,

`(y + 3)^2 = 36`

            ` y = -3+- 6`

                = -9 , 3

We will neglect the negative value. So,

y = -9 , 3