A line is of length 10 units and one of its ends is (- 2, 3). If the ordinate of the other end is 9, prove that the absicca of the other end is 6 or - 10.

Given that the line has length of 10 units and one of its ends is (- 2, 3).

It is also given that the ordinate of the other end is 9. Let us assume the other end is (x, 9).

We know that distance(S) between the points (x₁, y₁) and (x₂, y₂) is

⇒

⇒ 10 = (x + 2)² + (- 6)²

⇒ 100 = (x + 2)² + 36

⇒ (x + 2)² = 64

⇒ x + 2 = ±8

⇒ x = - 2 + 8 (or) x = - 2 - 8

⇒ x = 6 or 10

∴ Thus proved.