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, the distance between points (p, -5) and (2, 7) is 13 units.

$\because$ The distance between two points $(x_1,y_1)\text{and}(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

$\Rightarrow (2-p{)}^2+(7+5{)}^2={13}^2$

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

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

$\Rightarrow 2-p=\pm 5$

case 1:
$2-p=5\Rightarrow p=-3$

case 2:
$2-p=-5\Rightarrow p=7$

$p$ can be -3 or 7