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?
Answer & explanation
Correct answer: option 3
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