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
By the distance formula, the square of the distance between two points is the sum of the squares of the differences of their x- and y-coordinates.
The distance formula (the x-difference is \(5-2\) and the y-difference is \(k-(-2)=k+2\)):
\((5-2)^2+(k+2)^2=5^2\)
\(9+(k+2)^2=25\)
\((k+2)^2=16\)
Solving for \(k\) (a square is 16 when the number is 4 or \(-4\)):
\(k+2=4\) or \(k+2=-4\)
\(k=2\) or \(k=-6\)
Only 2 is among the options