Question

Find the values of k, if the distance between the points (1,4) and (k, 1) is 5​

Answer 1

Step-by-step explanation:

bro use distance formula and find answer

Answer 2

The values of k = - 3 , 5

Given :

The distance between the points (1,4) and (k, 1) is 5

To find :

The value of k

Formula Used :

For the given two points ( x₁ , y₁) & (x₂ , y₂) the distance between the points

$= \sf{ \sqrt{ {(x_2 -x_1 )}^{2} + {(y_2 -y_1 )}^{2} } }$

Solution :

Step 1 of 2 :

Form the equation to find the value of k

Here it is given that the distance between the points (1,4) and (k, 1) is 5

So by the given condition

$\displaystyle \sf \sqrt{ {(k - 1)}^{2} + {(1 - 4)}^{2} } = 5$

Step 2 of 2 :

Find the value of k

$\displaystyle \sf \sqrt{ {(k - 1)}^{2} + {(1 - 4)}^{2} } = 5$

$\displaystyle \sf{ \implies }{(k - 1)}^{2} + {( - 3)}^{2} = {5}^{2}$

$\displaystyle \sf{ \implies }{(k - 1)}^{2} + 9 = 25$

$\displaystyle \sf{ \implies }{(k - 1)}^{2} = 16$

$\displaystyle \sf{ \implies }{(k - 1)}^{2} = {4}^{2}$

$\displaystyle \sf{ \implies }{(k - 1)}^{} = \pm \: 4$

Now ,

k - 1 = 4 gives k = 5

k - 1 = - 4 gives k = - 3

Hence the values of k = - 3 , 5

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