Question

The distance between $(x,3)$ and $(4,5)$ is $2\sqrt{5}units$ then $x=$

• A. $8$
• B. $2$
• C. $4$
• D. $0$

Answer 1

Answer: (A), (D)

$0$
$8$

Given that, the distance between $(x,3)$ and $(4,5)$ is $2\sqrt{5},$

To find the value of $x$

Distance between two points is given by

$d=\sqrt{(x-4{)}^2+(3-5{)}^2}$

$\Rightarrow 2\sqrt{5}=\sqrt{(x-4{)}^2+(-2{)}^2}$

$\Rightarrow 2\sqrt{5}=\sqrt{(x-4{)}^2+4}$

Squaring both sides, we get

$\Rightarrow 4\times 5=(x-4{)}^2+4$

$\Rightarrow 20-4=(x-4{)}^2$

$\Rightarrow 16=(x-4{)}^2$

$\Rightarrow (x-4{)}^2=16$

$\Rightarrow (x-4)=\pm 4$

$\Rightarrow x=4\pm 4$

$\therefore x=8,0$

Hence, the value of $x$ is $8,0$