Question

Find the value of a if the distance between the points (5 , a) and (1 , 5) is 5 units .

Answer 1

Let the points (5 ,a) and (1 , -5) be P and Q  respectively.

Given , PQ = 5 units 

`sqrt ((5 - 1)^2 + ("a" + 5)^2) = 5`

squaring both sides , we get ,

16 + a² + 25 + 10"a" = 25

⇒ a² + 10a + 16 = 0

⇒ a² + 8a + 2a + 16 = 0

⇒ (a + 8)(a + 2) = 0

∴ a = - 8 , - 2