The features of Δ ABC D. It is scalene, B. It is isosceles. Therefore, D. It is scalene, B. It is isosceles is correct.
Let's analyze the features of triangle ABC with vertices A(3,3), B(4,7), and C(8,6).
A. It is a right triangle:
To determine if the triangle is right-angled, we can check if the slopes of any two sides multiply to give -1.
The slope of AB is (7-3)/(4-3) = 4, and the slope of BC is (6-7)/(8-4) = -0.25. These slopes do not multiply to -1, so the triangle is not a right triangle.
B. It is isosceles:
An isosceles triangle has at least two sides of equal length.
We can find the distances between the vertices to check this.
The distance between A and B is √((4-3)² + (7-3)²) = √17.
The distance between B and C is √((8-4)² + (6-7)²) = √17. So, AB and BC are of equal length, making the triangle isosceles.
C. It is equilateral:
An equilateral triangle has all sides of equal length. As AB and BC are not equal, the triangle is not equilateral.
D. It is scalene:
A scalene triangle has all sides of different lengths.
Since AB and BC are of different lengths, the triangle is scalene.
E. It is equiangular:
An equiangular triangle has all angles equal.
To determine this, we would need to calculate the angles, but it's not necessary given the previous findings.
If the triangle is isosceles, it cannot be equiangular.