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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
Solution
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
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