Distance between two points $( x,\ 7)$ and $( 1,\ 15)$ is $10\ units$ find the value of $x$.

Given: Distance between two points $( x,\ 7)$ and $( 1,\ 15)$ is $10\ units$.

To do: To find the value of $x$.

Solution:

Here $x_1=x,\ y_1=7,\ x_2=1,\ y_2=15$, 

Distance between the given points$=10\ units$

On using the distance formula,

$10=\sqrt{( x_2-x_1)^2+( y_2-y_1)^2}$

$\Rightarrow 10=\sqrt{( 1-x)^2+( 15-7)^2}$

$\Rightarrow 10=\sqrt{( 1-x)^2+8^2}$

$\Rightarrow 10=\sqrt{( 1-x)^2+64}$

$\Rightarrow 100=( 1-x)^2+64$

$\Rightarrow ( 1-x)^2=100-64$

$\Rightarrow ( 1-x)^2=36$

$\Rightarrow 1-x=\pm\sqrt{36}$

$\Rightarrow 1-x=\pm6$

If $1-x=6$

$\Rightarrow x=1-6=-5$

If $1-x=-6$

$x=1+6=7$

Thus, $x=-5,\ 7$

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Updated on: 10-Oct-2022

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