Logically there will only be 2 possible points for C
1.Find the equation for the straight line that pass A and C
you will get y = x - 1
2.We know that the triangle is isosceles triangle since AB = AC
So its mean that equation for straight line of AB is y = -x + 1
3.Actually 1. and 2. doesnt matter in this question..XD
As long as you know that B and C₁ is a straight line that parallel to y-axis and B and C₂ is a straight line that parallel to x-axis
4.So, you just need to use pythagoras theorem in this case...
You will get half the distance of BC₁ and BC₂ is 2 unit
5.Then, the coordinates of C are obviously C₁(-1,-2) and C₂(3,2)
I am sorry if my answer is not in your syllabus.