Question

Find all possible values of x for which the distance between the points A(x, –1) and B(5, 3) is 5 units.

Answer 1

Given AB = 5 units 

Therefore, (AB)² = 25 units 

`⇒(5-a)^2 +{3-(-1)}^2 = 25`

`⇒(5-a)^2+(3+1)^2 = 25`

`⇒(5-a)^2 + (4)^2 =25`

`⇒(5-a)^2 +16 =25`

`⇒(5-a)^2 =25-16`

`⇒(5-a)^2 = 9`

`⇒(5-a)=+-sqrt(9)`

`⇒ 5-a=+-3`

`⇒5-a =3 or 5-a=-3`

`⇒ a=2 or 8`

Therefore, a = 2 or 8.