Question

Find the $x$ so that the distance between the points $(-2,-3)$ and $(-3,x)$ is equal to $5$.

• A. $x=-3\pm 2\sqrt{6}$
  
• B. $x=-3+2\sqrt{6}$
  
• C. $x=\pm 3\pm 2\sqrt{6}$
  
• D. $x=-3\pm 2\sqrt{6}$
  

Answer 1

The correct option is A

$x=-3\pm 2\sqrt{6}$

The distance between points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

So, the distance between points $(-2,-3)$ and $(-3,x)$ will be

$\sqrt{{(-2+3)}^2+{(x+3)}^2}=5$

$\Rightarrow (x+3{)}^2+1=25$

$\Rightarrow (x+3{)}^2=25-1=24$

$\Rightarrow x+3=\pm \sqrt{24}=\pm 2\sqrt{6}$

Take square root both sides

$\therefore x=-3\pm 2\sqrt{6}$