The points (x, 2) is equidistant from (8, -2) and (2, -2). Find the va

1.	The points (x, 2) is equidistant from (8, -2) and (2, -2). Find the value of x.
Answer» Let A = (2, 2) B = (8, -2) C = (2, -2) By data AB = AC = AB² = AC² ⇒ (8 – x)² + (-2 -2)² = (x – 2)² + (2 + 2)² 64 + x² + 16x + 16 = x² + 4 - 4x + 16 -16x + 4x = 4 -64 ⇒ – 12x = -60 ∴ x = 5

The points (x, 2) is equidistant from (8, -2) and (2, -2). Find the value of x.

Answer»

Let A = (2, 2) B = (8, -2) C = (2, -2)

By data AB = AC = AB² = AC²

⇒ (8 – x)² + (-2 -2)² = (x – 2)² + (2 + 2)²

64 + x² + 16x + 16 = x² + 4 - 4x + 16

-16x + 4x = 4 -64 ⇒ – 12x = -60

∴ x = 5