If the distance between the points (4, 8) and (k, -4) is 13 units, then which one of the following can be the value of k?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → -1
By the distance formula, the distance between \((x_1, y_1)\) and \((x_2, y_2)\) is \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\). Setting it equal to 13 gives an equation in \(k\).
\((k-4)^2+(-4-8)^2=13^2\)
\((k-4)^2+144=169\)
\((k-4)^2=25\), so \(k-4=5\) or \(k-4=-5\)
\(k=9\) or \(k=-1\)
Only \(-1\) is among the options; \(k=9\) gives the other point, (9, −4), at the same distance.