Question

Find the value of k such that (1, k) is equidistant from (0, 0) and
(5, 6).

k =

Answer 1

Step-by-step explanation:

Since, (1, k) is equidistant from (0,0) & (5, 6)

Therefore by distance formula, we have:

Distance between (1, k) & (0, 0) = Distance between (1, k) & (5, 6)

Hence,

$\sqrt{(1 - 0)^{2} + (k - 0)^{2} } = \sqrt{(1 - 5)^{2} + (k - 6)^{2} } \\ \sqrt{(1)^{2} + (k )^{2} } = \sqrt{( - 4)^{2} + (k - 6)^{2} } \\ squiring \: both \: sides \: we \: find : \\ 1 + {k}^{2} = 16 + (k - 6) ^{2} \\ 1 + {k}^{2} = 16 + k^{2} - 12k + 36 \\ k^{2} - 12k + 52 - k^{2} - 1 = 0 \\ - 12k + 51 = 0 \\ 12k = 51 \\ k = \frac{51}{12} \\ k = \frac{17}{4} \\ k = 4 \frac{1}{4}$