Question

find the vertices of K if [0,2] is equidistant from [1,K] and [K ,5]

Answer 1

here is your answer mate

Answer 2

Answer:

$\sf {The \:Distance\: Formula:}$

$\tt {\sqrt {(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}}$

Taking the points [0,2] and [1,k] first:

Distance = $\tt {\sqrt {(1-0)^{2} + (k-2)^{2}}}$

=》 $\tt {\sqrt {1 + k^{2} + 4 - 4k}}$ ... (1)

Taking the points [0,2] and [k,5] next:

Distance = $\tt {\sqrt {(k-0)^{2} + (5-2)^{2}}}$

=》 $\tt {\sqrt {k^{2} + 9}}$ ... (2)

(1) = (2)

$\tt {\sqrt {1 + k^{2} + 4 - 4k}}$ = $\tt {\sqrt {k^{2} + 9}}$

Squaring on both sides :

$\tt {k^{2} + 5 - 4k = k^{2} + 9}$

5 - 9 = 4k

$\tt {\huge {k = (-1)}}$