Question

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

Answer 1

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Answer 2

Step-by-step explanation:

We know that :

Distance between two points (x₁ , y₁) and (x₂ , y₂) is given by :

$\bigstar\;\;\mathsf{Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}$

Given : Points are (4 , k) and (1 , 0)

where : x₁ = 4 and x₂ = 1 and y₁ = k and y₂ = 0

Given : Distance between the points (4 , k) and (1 , 0) is 5

Substituting the given values in the Distance formula, We get :

$\implies \mathsf{\sqrt{(1 - 4)^2 + (0 - k)^2} = 5}$

Squaring on both sides, We get :

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

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

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

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

$\implies \mathsf{k^2 = 16}$

$\implies \mathsf{k = \sqrt{16}}$

$\implies \mathsf{k = \sqrt{(\pm\;4)^2}}$

$\implies \mathsf{k = \pm\;4}}$

Answer : Possible values of k are ± 4