Question

The distance between the points (2,-3) and (k,9) is 13units find k​

Answer 1

SoluTion:

Given points :

• $\sf{2, -3}$

• $\sf{k, 9}$

• Distance = 13 units

We have to find the value of k.

We know that,

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

Here, $\sf{x_{1} = 2, x_{2} = k, y_{1} = -3\:and\:y_{2} = 9}$

Putting the values,

: $\implies$ 13 = $\sf{\sqrt{(k - 2)^{2} + (9 + 3)^2}}$

: $\implies$ 13 = $\sf{\sqrt{(k - 2)^{2} + (12)^2}}$

Squaring both sides,

: $\implies$ $\sf{13^{2} = ( \sqrt{(k - 2)^2 + (12)^{2})^2}}$

: $\implies$ $\sf{169 = (k - 2)^2 + 144}$

: $\implies$ $\sf{(k - 2)^{2} = 169 - 144}$

: $\implies$ $\sf{(k - 2)^{2} = 25}$

: $\implies$ $\sf{(k - 2) = \sqrt{25}}$

: $\implies$ $\sf{(k - 2) = 5}$

: $\implies$ $\sf{k = 5 + 2}$

: $\implies$ $\blue{\sf{k = 7}}$

Hence, value of k is 7.