If the distance between the points (2, -2) and (5, k) is 5 units, then one of the possible values of k shall be which of the following?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2
Let the two points be $A = (2, -2)$ and $B = (5, k)$.
Using the distance formula:
$\sqrt{(5 - 2)^2 + (k + 2)^2} = 5$
$\sqrt{9 + (k + 2)^2} = 5$
$9 + (k + 2)^2 = 25$
$(k + 2)^2 = 16$
$k + 2 = \pm 4$
Therefore, $k = 2$ or $k = -6$
One of the possible values of $k$ is: 2