Question

Determine k,sabendo que a distancia entre os pontos p(-8,k) e Q(k-1,-5) e 10

Answer 1

100= (k-1-[-8])^(2) + (-5-k)^(2)
100= (k-1+8)^(2) + (-5-k) ×(-5-k)
100= (k-1+8)^(2) + 25 +5k+5k + k^(2)
100= (k-1+8)^(2) +25+10k +k^(2)
100= (k+7)^(2) +25+10k +k^(2)
100= (k+7)×(k+7)+25+10k +k^(2)
100= k^(2) +7k +7k +49 +25+10k +k^(2)
100= 2k^(2) +24k + 74
50= k^(2) +12k+ 37
k^(2) +12k -13= 0

delta= B^(2) -4AC
delta= 12^(2)- 4×1×(-13)
delta =144 +52
delta=196

K=( -B + - raiz de delta)÷ 2A
k= (-12+ - raiz de 196) ÷2×1
k= (-12 + - 14) ÷2

k1 = (-12+14) ÷2
k1= 2÷2
k1= 1

k2= (-12-14)÷2
k2= -26÷2
k2= -13