The distance between the points (4, 8) and (k, -4) is 13. What is the value of k?

Answer: Option C

Distance formula between two points
Distance = $$\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$$
⇒ 13 = $$\sqrt{{\left(k-4\right)}^2+{\left(-4-8\right)}^2}$$
⇒ 169 = k² + 16 - 8k + 144
⇒ k² - 8k - 9 = 0
⇒ k² - 9k + k - 9 = 0
⇒ k(k - 9) + 1(k - 9) = 0
⇒ (k + 1)(k - 9) = 0
⇒ k = -1 and 9
∴ k = -1 (According to options)