Question

If the distance between points (p, –5) and (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

Distance between points $(x_1,y_1)$ and $(x_2,y_2)$

= $\sqrt{(x_2-x_1{)}^2-(y_2-y_1{)}^2}$

$\Rightarrow$ Distance between points (p, –5) and (2, 7) = 13 units

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

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

$\Rightarrow {(2-p)}^2={13}^2-{12}^2$

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

$\Rightarrow 2-p=\pm 5$

$\Rightarrow p=7or-3$