# Find all real numbers k such that $||k (1,1) - (3, -2)|| = \sqrt {37}$

Find all real numbers $k$ such that $|| k (1, 1) - (3, -2) || = \sqrt{37}.$
Ok. Am I supposed to go and manually plug in random number( which sounds terrible) or is there another way?

I could really use some tips to get started. Thank you!

• Well, what is $||(a,b)||$? – lulu Sep 11 '17 at 13:29
• – Shaun Sep 11 '17 at 13:39

If you mean by $||(a,b)||=\sqrt{a^2+b^2}$ then :
$$\sqrt{37}=||k(1,1)-(3,-2)||=||(k,k)+(-3+2)||=||(k-3,k+2)||=\sqrt{(k-3)^2+(k+2)^2}$$
Thus $(k-3)^2+(k+2)^2=37$
Continue it from here to find $k$