Question

Find the value of $x_1$ if the distance between the points $(x_1,2)$ and $(3,4)$ be $8$.

• A. $3\pm 2\sqrt{15}$
• B. $3\pm \sqrt{15}$
• C. $2\pm 3\sqrt{15}$
• D. $2\pm \sqrt{15}$

Answer 1

The correct option is A $3\pm 2\sqrt{15}$

The given points are $(x_1,2)$ and $(3,4)$.

The distance between the points are $8.$

Here, $x_1=x_1,y_1=2,x_2=3$ and $y_2=4$

Distance between the points $=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

$\Rightarrow$ $8=\sqrt{(3-x_1{)}^2+(4-2{)}^2}$

$\Rightarrow$ $8=\sqrt{(3-x_1{)}^2+4}$

$\Rightarrow$ $64=(3-x_1{)}^2+4$ [ Taking square on both sides ]

$\Rightarrow$ $60=(3-x_1{)}^2$

$\Rightarrow$ $\pm 2\sqrt{15}=3-x_1$

$\therefore$ $x_1=3\pm 2\sqrt{15}$