Question

Find the value of $x$ if the distance between the points $(2,-11)$ and $(x,-3)$ is $10$ units.

• A. $6$
• B. $8$
• C. $9$
• D. $4$

Answer 1

The correct option is B $8$

Distance between two points $=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$
Distance between the points $(2,-11)$ and $(x,-3)=10$

$\Rightarrow \sqrt{{(x-2)}^2+{(-3+11)}^2}=10$

$\Rightarrow \sqrt{{(x-2)}^2+8^2}=10$

$\Rightarrow {(x-2)}^2+64=100$

$\Rightarrow {(x-2)}^2=36$

$\Rightarrow x-2=+6$ or $-6$

$\Rightarrow x=8$ or $-4$