Question

If the distance between the points (–5, 7) and (11, –x) is 20, then the value of x can be

• A. 5
• B. 7
• C. 8
• D. 6

Answer 1

The correct option is A 5

Using the distance formula, the distance between the points (–5, 7) and (11, –x) is

$=\sqrt{(11+5{)}^2+(-x-7{)}^2}=20$

$\Rightarrow {16}^2+(-x-7{)}^2={20}^2$

$\Rightarrow (-x-7{)}^2={20}^2-{16}^2$

$\Rightarrow (-x-7{)}^2=(20+16\left)\right(20-16)$

$\Rightarrow (-x-7{)}^2=36\times 4$

$\Rightarrow (-x-7{)}^2=(12{)}^2$

$\Rightarrow -x-7=\pm 12$

$\Rightarrow -x-7=12or-x-7=-12$

$\Rightarrow x=-19orx=5$

Hence, the correct answer is option (a).