Question

The distance between the points (−1,4) and (3,k) is square root 20 By forming an equation in , find the possible values of k.

Answer 1

Given ,

• The distance between the points A(−1,4) and B(3,k) is square root 20.

To find :-

• The value of k .

A/Q,

$\sqrt{(3 - ( - 1))^{2} + {(k - 4)}^{2} } = \sqrt{20}$

$\implies \sqrt{(3 + 1)^{2} + {(k - 4)}^{2} } = \sqrt{20}$

$\implies {(4)^{2} + {(k - 4)}^{2} } = 20$

$\implies 16 + {k}^{2} - 8k + 16 = 20$

$\implies {k}^{2} - 8k +32 - 20 = 0$

$\implies {k}^{2} - 8k +12 = 0$

$\implies {k}^{2} - 6k - 2k +12 = 0$

$\implies k(k - 6)- 2(k - 6) = 0$

$\implies (k - 6)(k - 2) = 0$

$\implies k - 6 = 0 \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: k - 2 = 0$

$\implies \boxed {\bold{k = 6\: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: k = 2}}$