Question

If the distance between points $(p,-5),(2,7)$ is $13$ units, then $p$ is

• A. $-3$ or $7$
• B. $-7$ or $3$
• C. $-3$ or $-7$
• D. $3$ or $7$

Answer 1

The correct option is A $-3$ or $7$

Given, Distance between the points $(p,-5)$ and $(2,7)=13$
The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ can be calculated as $\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$\therefore$ Distance between the points $(p,-5)$ and $(2,7)=\sqrt{{(2-p)}^2+{(7-(-5\left)\right)}^2}$

$\Rightarrow \sqrt{{(2-p)}^2+144}=13$

$\Rightarrow (2-p{)}^2+144=169$

$\Rightarrow$ $(2-p{)}^2=25$

$\Rightarrow 2-p=5$ or $2-p=-5$

$\therefore p=-3$ or $p=7$