Question

If the distance between the points $P(-3,5)$ and $Q(-x,-2)$ is $\sqrt{58}$, then find the value(s) of $x.$

• A. $x=6$ or $x=0$
• B. $x=3$ or $x=-3$
• C. $x=9$ or $x=3$
• D. None of these

Answer 1

The correct option is A $x=6$ or $x=0$

The distance between points $(x_1,y_1)$ and $(x_2,y_2)$ is given by

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

So, by using distance formula,

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

$\Rightarrow \sqrt{58}=\sqrt{x^2+9-6x+49}$

$\Rightarrow 58=x^2-6x+58$

$\Rightarrow x^2-6x=0$

$\Rightarrow x^2=6x$

$\Rightarrow x=0,6$