Question

На координатной плоскости вершины треугольника ABC имеют координаты A(-1; 3); B(3; 6); C(3; 3); Тогда этот треугольник...????

Answer 1

Этот треугольник авс прямоугольный 
угол асв примой

Answer 2

Triangle ABC on the Coordinate Plane

The coordinates of the vertices of triangle ABC on the coordinate plane are as follows: - Vertex A: (-1, 3) - Vertex B: (3, 6) - Vertex C: (3, 3)

To determine the characteristics of this triangle, we can analyze its sides, angles, and other properties.

Side Lengths

To find the lengths of the sides of triangle ABC, we can use the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by the formula:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can calculate the lengths of the sides of triangle ABC:

- Side AB: Distance between A(-1, 3) and B(3, 6) - Side BC: Distance between B(3, 6) and C(3, 3) - Side CA: Distance between C(3, 3) and A(-1, 3)

Let's calculate the lengths of these sides:

- Side AB: sqrt((3 - (-1))^2 + (6 - 3)^2) = sqrt(16 + 9) = sqrt(25) = 5 - Side BC: sqrt((3 - 3)^2 + (3 - 6)^2) = sqrt(0 + 9) = sqrt(9) = 3 - Side CA: sqrt((-1 - 3)^2 + (3 - 3)^2) = sqrt(16 + 0) = sqrt(16) = 4

Therefore, the lengths of the sides of triangle ABC are as follows: - Side AB: 5 - Side BC: 3 - Side CA: 4

Angles

To find the angles of triangle ABC, we can use various methods such as the Law of Cosines or trigonometric functions. However, in this case, we can use the fact that triangle ABC is a right triangle.

Since the coordinates of the vertices are A(-1, 3), B(3, 6), and C(3, 3), we can see that side AB is vertical and side BC is horizontal. Therefore, angle ABC is a right angle.

Conclusion

Based on the given coordinates, we can conclude that triangle ABC is a right triangle with side lengths of 5, 3, and 4. The right angle is at vertex B, which is the angle opposite side BC.

Please let me know if there's anything else I can help you with!