Question

the distance between two points (2,8) and (2,k) is 3 then find the k value​

Answer 1

Given:

↬ Two points- A(2,8) and b(2,k)

↬ Distance between the given points is 3

To Find:

• Value of 'k'

➺ Formula to be known before solving question

• If two points having coordinate $(\sf\bold{x_{1} ,y_{1} })$ and $(\sf\bold{x_{2} ,y_{2} })$ are given, then distance between these points are given by

$\boxed{\sf{Distance\:formula=\sqrt{(x_{2}-x_{1} ) ^{2}+(y_{2}-y_{1} )^{2}}}}$

Solution:

Using distance formula,

$\sf{Distance\:between\:A\:and\:B=\sqrt{(2-2) ^{2}+(k-8)^{2}}}$

$\sf{Distance\:between\:A\:and\:B=\sqrt{(0)^{2}+(k-8)^{2}}}$

$\sf{Distance\:between\:A\:and\:B=\sqrt{(k-8)^{2}}}$

$\sf{Distance\:between\:A\:and\:B=k-8}$

It is also given that,

$\sf{Distance\:between\:A\:and\:B=3}$

Therefore,

$\leadsto\sf{k-8=3}$

$\leadsto\sf{k=8+3}$

$\leadsto\sf\pink{k=11}$

Hence, the value of k is 11.