At points A (-4; 8), B (-12; 11) C (-7; 0) are the vertices of the triangle. Determine the type of triangle.

1. Find the sides of the triangle:
A (-4; 8);
B (-12; 11);
C (-7; 0);
AB = √ ((x (B) – x (A)) ^ 2 + (y (B) – y (A)) ^ 2);
AB = √ ((- 12 + 4) ^ 2 + (11 – 8) ^ 2) = √ ((- 8) ^ 2 + 3 ^ 2) = √ (64 + 9) = √73;
AC = √ ((x (C) – x (A)) ^ 2 + (y (C) – y (A)) ^ 2);
AC = √ ((- 7 + 4) ^ 2 + (0 – 8) ^ 2) = √ ((- 3) ^ 2 + (-8) ^ 2) = √ (9 + 64) = √73;
BC = √ ((x (C) – x (B)) ^ 2 + (y (C) – y (B)) ^ 2);
BC = √ ((- 7 + 12) ^ 2 + (0 – 11) ^ 2) = √ (5 ^ 2 + (-11) ^ 2) = √ (25 + 121) = √146.
2. The triangle is isosceles and rectangular:
AB = AC = √73;
AB ^ 2 + AC ^ 2 = 2 * (√73) ^ 2 = 2 * 73 = 146 = (√146) ^ 2 = BC ^ 2.
Answer: isosceles and rectangular.