Question

The distance between the points (−3, 2) and (x, 10) is 10 units. The value of x is ______.

Options

• 3

• −9

• 3 or −9

• 3 and −9

Answer 1

The distance between the points (−3, 2) and (x, 10) is 10 units. The value of x is 3 or −9.

Explanation:

\[\sqrt{(x+3)^2+(10-2)^2}=10\Rightarrow (x+3)^2+64=100.\] Thus \[(x+3)^2=36\Rightarrow x+3=\pm6,\] giving \[x=3\text{ or }x=-9.\] Option (iii) is correct.