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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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