1. The problem states that there isn't a right-angled triangle between points A, B, and C. 2. To verify if a triangle is right-angled, we use the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse (the longest side). 3. Calculate the lengths of sides AB, BC, and AC using the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$. 4. Check if any combination of these side lengths satisfies the Pythagorean theorem. 5. If none satisfy, then the triangle is not right-angled, confirming the statement. 6. This method ensures a clear, mathematical verification rather than assumption.