Question

The value of $x$ if the distance between the points $(x,4)$ and $(-5,3)$ is equal to $5$.

• A. $x=-5\pm 2\sqrt{6}$
• B. $x=-5\pm 2\sqrt{5}$
• C. $x=-5\pm 2\sqrt{23}$
• D. $x=-5\pm 2\sqrt{7}$

Answer 1

The correct option is A $x=-5\pm 2\sqrt{6}$

Let $A(x,4)$ and $B(-5,3)$. Then it is given that $AB=5units$. Therefore, $\sqrt{(x+5{)}^2+(4-3{)}^2}=5$ or $(x+5{)}^2+1=25$ or $(x+5{)}^2=24$ or $x+5=\pm 2\sqrt{6}$ or $x=-5\pm 2\sqrt{6}$. Thus we get two values of x satisfying the above condition.