Question

Determine o valor de K para que m(-4,K) seja equidistante de n(-1,5) e p(-2,6). é prova genteee, please respondam certo....vle 99 pts

Answer 1

Dnm=Dpm
(-1-4)²+(5+k)²=(-2-4)²+(k-6)²
25+5²-2.5.k+k²=36+k²-2.k.-6+6²
25+25-10k+k²=36+k²+12k+36
k²-10k+50=k²+12k+72        (corta o ''k'')
-22k=22
k=-1

Answer 2

Para serem equidistantes, as hipotenusas formadas pelos triangulos-retangulos do ponto P e N deve ser iguais:

(P):
$a^2=2^2+(6-k)^2$

(N)
$a^2=3^2+(5-k)^2$

Igualando as duas:
$3^2+(5-k)^2=2^2+(6-k)^2\\\\(5-k)^2-(6-k)^2=2^2-3^2\\\\25-10k+k^2-36+12k-k^2=-5\\\\2k=-5+11\\\\k=\frac{6}{2}=3$

Resposta: k = 3