Find ‘a’ if the distance between the points (a, 2) and (3, 4) is V

1.	Find ‘a’ if the distance between the points (a, 2) and (3, 4) is V8 units.
Answer» Let P = (a, 2) and Q = (3, 4) By data \|PQ\| = √8 ⇒ √8 = √((3 - a)² + (4 - 2)²) ⇒ 8 = (3 – a)² + 2² = 8 ⇒ 9 + a² – 6a + 4 ⇒ a² – 6a + 5 = 0 ⇒ (a – 5)(a – 1) = 0 ⇒ a = 5 or a = 1

Find ‘a’ if the distance between the points (a, 2) and (3, 4) is V8 units.

Answer»

Let P = (a, 2) and Q = (3, 4)

By data |PQ| = √8

⇒ √8 = √((3 - a)² + (4 - 2)²)

⇒ 8 = (3 – a)² + 2² = 8

⇒ 9 + a² – 6a + 4

⇒ a² – 6a + 5 = 0

⇒ (a – 5)(a – 1) = 0

⇒ a = 5 or a = 1