Question

The value of k for which the point (–4, k) is at a distance of 10 units from (2, 4) is .

• A. 12,-4
• B. 12,4
• C. -12,-4
• D. -12,4

Answer 1

The correct option is A 12,-4

Let A(-4, k) and B(2, 4) be the points.
AB=10 units (Given)
$\Rightarrow A{B}^2=100\therefore \mathrm{By}\mathrm{using}\mathrm{distance}\mathrm{formula}:(2-(-4){)}^2+(4-k{)}^2=100\Rightarrow 36+16+k^2-8k=100\Rightarrow k^2-8k-48=0\Rightarrow (k-12)(k+4)=0\Rightarrow k=12,-4$