Find the slope of line L

Question

A straight line ($L$) passing through the point $A(1,2)$ meets the line $x+y=4$ at the point $B$. If $AB=\sqrt 2$, what is the slope of $L$?

With some help I did it and the slope comes out to be 2+√3 or 2-√3

Answer 1

Let $B(x,y)$. You look for the slope $$ \frac{y-2}{x-1} $$

and $x+y = 4$, and $2 = AB^2 = (x - 1)^2 + (y-2)^2$.

Can you take it from here?

Answer 2

Let the coordinate of point $B$ be $(a,4-a)$

Given that $AB=\sqrt2$. Solve for $a$

Then you will get coordinate of B and you have already coordinate of A. You can get the slope very easily.