Question

if the distance between the points (x,2) and (3,-6) is 10units then the value of x is​

Answer 1

Given,

Distance between points $\[ = 10\,unit\]$

Points, $\[\left( {x,2} \right),\left( {3, - 6} \right)\]$

Solution,

The distance between the points $\[\left( {{x_1},{y_1}} \right),\left( {{x_2},{y_2}} \right)\]$ ,

$\[ = \sqrt {{{\left( {{y_2} - {y_1}} \right)}^2} + {{\left( {{x_2} - {x_1}} \right)}^2}} \]$

According to the question,

$\[\sqrt {{{\left( {2 + 6} \right)}^2} + {{\left( {3 - x} \right)}^2}} = 10\]$

$\[ \Rightarrow 64 + {\left( {3 - x} \right)^2} = 100\]$

$\[ \Rightarrow {\left( {3 - x} \right)^2} = 36\]$

$\[ \Rightarrow \left( {3 - x} \right) = 6\]$

$\[ \Rightarrow x = - 3\]$

Hence the value of x is $\[ - 3\]$.