Question

if the distance between points is a 4 k and b 7 6 is 6 unit then find the value k
plz tell me this answer

Answer 1

Answer:

$\red { Value \:of \:k } \green {= 6±3\sqrt{3}}$

Step-by-step explanation:

$Given \: two \: points \: A(4,k) ,\:and \: B(7,6)$

$Let \: A(4,k) = (x_{1},y_{1}) \:and \\B(7,6) = (x_{2},y_{2})$

$\boxed { \pink { Distance (AB) = \sqrt{(x_{2} -x_{1})^{2} + (y_{2} -y_{1})^{2}}}}$

$AB = 6 \:(given)$

$\implies AB^{2} = 6^{2}$

$\implies ( 7-4)^{2} + (6-k)^{2} = 36$

$\implies 3^{2} + (6-k)^{2} = 36$

$\implies (6-k)^{2} = 36 - 9$

$\implies (k-6)^{2} = 27$

$\implies (k-6)= ±\sqrt{27}$

$\implies k= 6±3\sqrt{3}$

Therefore.,

$\red { Value \:of \:k } \green {= 6±3\sqrt{3}}$

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