Question

if the distance between the two points A(4,k) and B(1,0) is 5 then what can be the possible values of k

Answer 1

according to distance formula

Answer 2

Answer:

$Value \: of \: k = ±4$

Step-by-step explanation:

$Given \:distance \: between\: two\: points\\A(4,5)\:and\:B(1,0) \:is \:5$

$Here, x_{1}=4 ; \: y_{1}=k \\</p><p>x_{2}=1 ; \: y_{2}=0$

$By\: Distance \: formula:\\</p><p>\boxed {Distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}$

$AB^{2}=5^{2}$

$\implies (x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}=25$

$\implies (1-4)^{2}+(0-k)^{2}=25$

$\implies (-3)^{2}+k^{2}=25$

$\implies 9+k^{2}=25$

$\implies k^{2}=25-9$

$\implies k^{2}=16$

$\implies k = ±\sqrt{4^{2}}$

$\implies k = ±4$

Therefore,

$Value \: of \: k = ±4$

•••♪