The correct option is C Right-isosceles triangle
Let the triangle formed by the points (1, 5), (4, 2) and (–2, 2) be ABC where A be (1, 5), B be (4, 2) and C be (–2, 2).
AB=√(4−1)2+(2−5)2=3√2 units
BC=√(−2−4)2+(2−2)2=6 units
AC=√(−2−1)2+(2−5)2=3√2 units
Now,
AB2+AC2=3√2)2+(3√2)2=18+18=36=62=BC2
Therefore, ΔABC is a right-angled at A.
Also, AB=AC=3√2 units.
Thus, ΔABC is a right-isosceles triangle.
Hence, the correct answer is option (c).