Points M (3; 1), K (0; 0), P (0; 2) are given. Will the MPK triangle be equilateral?

It is known that the distance d between the points (x1; y1) and (x2; y2) on the coordinate plane xOy can be determined by the formula d = √ [(x2 – x1) ^ 2 + (y2 – y1) ^ 2]. We have: КM = √ [(3 – 0) ^ 2 + (1 – 0) ^ 2] = √ (10), РМ = √ [(3 – 0) ^ 2 + (1 – 2) ^ 2] = √ (10) and КP = √ [(0 – 0) ^ 2 + (2 – 0) ^ 2] = 2. Therefore, the triangle MPK is not an equilateral triangle, since, although КМ = РМ, but КМ ≠ КР and РМ ≠ CD.