The vertices of the triangle A (1; 2), B (-5; 0), C (-1; -4) are given. Build a triangle, find its perimeter and angle B.

First, let’s find the length of each side of the ABC triangle.
AB = √ (-5 – 1) ^ 2 + (0 – 2) ^ 2 = 2√10.
Then AC = √ (-1 – 1) ^ 2 + (-4 – 2) ^ 2 = 2√10.
BC = √ (-1 + 5) ^ 2 + (-4 – 0) ^ 2 = 4√2.
Since the perimeter is the sum of all sides, the perimeter of the ABC triangle is: 4√10 + 4√2 = 4 (√10 + √2).
For the cosine theorem, we find the cosine of the angle B: (40 + 32 – 40) / (2 * 16√5) = √5 / 5, then the angle B is equal to 63.43о.