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

Solution (By Examveda Team)

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)