If distance between the points (4, 8) and (k, -4) is 13 unit, then which one of the following can be the value of k?

-1

We know that,

According to the distance formula, the distance between two points (x₁, y₁) and (x₂, y₂) can be computed as,

Distance = √[(x₂ – x₁)² + (y₂ – y₁)²]

Given,

 Distance between the points (4, 8) and (k, -4) is 13

⇒ (13)² = (k – 4)² + (–4 – 8)²

⇒ 169 = k² + 16 – 8k + 144

⇒ k² – 8k – 9 = 0

⇒ k² – 9k + k – 9 = 0

⇒ k(k – 9) + 1(k – 9) = 0

⇒ (k – 9) (k + 1) = 0

⇒ k = 9, -1

Value of k = -1