Three points on a grid form a triangle with sides of length A, B and C as shown in the example: y 10 9 8 7 6 5 C B 4 3 2 A 1 X 0 1 2 3 4 5 6 7 8 9 10 A triangle is said to be right-angled if the following test is true (where A is the length of the longest side): A2 = B2 + C2 A2 means A multiplied by A, for example 32 means 3 × 3 which evaluates to 9 You can calculate A2, B2 and C2 by using the coordinates of the endpoints of each line. For example, B2 is calculated as follows: y 10 9 8 7 P2 6 (Х2, У2) 5 B 4 3 P1 2 (Х₁, У₁) 1 X 0 1 2 3 4 5 6 7 8 9 10 The endpoints, P1 and P2, have the coordinates (3, 2) and (6, 6). The value B2 is given by the formula: B2 = (x₁ − x₂)2 + (y₁ – y₂)2 In this example: B2 = (3 – 6)2 + (2 – 6)2 B2 = (−3)2 + (−4)2 B2 = 9 + 16 B2 = 25