Final answer:
By using the distance formula to calculate the lengths of the sides and the Pythagorean theorem to check if the triangle satisfies the conditions of a right triangle, we can determine whether the given triangle is a right triangle or not.
Step-by-step explanation:
In order to classify the sides of the triangle and determine if it is a right triangle, we need to use the distance formula to find the lengths of the sides. The distance formula is given by d = sqrt((x2 - x1)^2 + (y2 - y1)^2). With this formula, we can calculate the lengths of sides AB, BC, and CA. Then, we can check if the triangle satisfies the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Calculating the lengths of the sides, we have: AB = sqrt((6 - 2)^2 + (3 - 3)^2) = 4, BC = sqrt((2 - 6)^2 + (7 - 3)^2) = 5, and CA = sqrt((2 - 2)^2 + (3 - 7)^2) = 4. Since AB^2 + BC^2 = 4^2 + 5^2 = 16 + 25 = 41, which is not equal to CA^2, the triangle is not a right triangle.