Question

Classify AABC by its sides. Then determine whether it is a right triangle,

A(6, 6), B(9, 3), C(2, 2)

Answer 1

Triangle ABC is a scalene triangle because all sides are of different lengths, and it is a right triangle as it satisfies the Pythagorean theorem (a² + b² = c²).

Step-by-step explanation:

To classify triangle ABC by its sides, we first need to determine the lengths of the sides using the distance formula: distance = √((x2 - x1)² + (y2 - y1)²).

For side AB:

distance = √((9 - 6)² + (3 - 6)²) = √(3² + (-3)²) = √(9 + 9) = √18

For side BC:

distance = √((9 - 2)² + (3 - 2)²) = √(7² + 1²) = √(49 + 1) = √50

For side CA:

distance = √((6 - 2)² + (6 - 2)²) = √(4² + 4²) = √(16 + 16) = √32

All sides are of different lengths, so triangle ABC is a scalene triangle. To determine whether it is a right triangle, we can use the Pythagorean theorem. We square the lengths of the sides and see if they satisfy the relation a² + b² = c², where c is the hypotenuse (longest side) and a and b are the other two sides.

So we check:

(√18)² + (√32)² = 18 + 32 = 50

(√50)² = 50

Since 18 + 32 equals 50, the triangle does satisfy the Pythagorean theorem and can be classified as a right triangle.