1. The problem is to analyze a right triangle on the Cartesian plane. 2. In a right triangle, one angle is $90^\circ$. 3. The Pythagorean theorem applies: $$a^2 + b^2 = c^2$$ where $a$ and $b$ are legs and $c$ is the hypotenuse. 4. To find the length of sides given coordinates, use the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 5. Identify the vertices of the triangle on the plane, calculate the lengths of the sides using the distance formula. 6. Verify the right angle by checking if the Pythagorean theorem holds. 7. This method helps understand the relationship between geometry and algebra on the Cartesian plane.