Question

find the x if the distance between (-8,x) and (2,0) is 5√5​

Answer 1

Let the points be

• A (-8, x)
• B (2, 0)

Applying distance formula,

AB = √[(x₂ - x₁)² + (y₂ - y₁)²]

Here:

• x₁ = -8
• x₂ = 2
• y₁ = x
• y₂ = 0

Substitute these values in the above formula

⇒ AB = √[(2 - (-8))² + (0 - x)²]

⇒ AB = √[(2 + 8)² + (-x)²]

⇒ AB = √[(10)² + x²]

⇒ AB = √(100 + x²)

⇒ 5√5 = √(100 + x²)

Squaring on both sides,

(5√5)² = 100 + x²

⇒ 125 = 100 + x²

⇒ 125 - 100 = x²

⇒ x² = 25

⇒ x = √25

∴ x = ±5