question_answer

If the distance between the points \[(4,k)\] and \[(1,0)\] is 5, then what can be the possible values of k?

Answer:

Distance between \[(4,k)\] and \[(1,0)=5\]

\[\sqrt{{{(1-4)}^{2}}+{{(0-k)}^{2}}}=5\]

On squaring both sides

\[9+{{k}^{2}}=25\]

or                     \[{{k}^{2}}=25-9=16\]

So                    \[k=\pm \,4\]