Question

ABC is righd triangle angle at B
if A is [-4,2] and B is [-1,2] Find c such that AC=5 units

Answer 1

See diagram.
C can be at two locations such that  AC = 5 units.

let C = (-1, y)
Then AC² = (y-2)²+(-1+4)²  = y²+ 4 -4y  + 9 = y² -4y +13  = 25 (given)
So  y² - 4 y - 12 = 0    it is easy to factorize it:
(y +2 ) (y -6) = 0        y = -2 or  +6.

So  C = (-1, -2)  or  (-1, +6)