Question

11. Select all the features of AABC.

8
9
et
2
y
0
B(4,7)
A(3, 3)
2
4
6
A. It is a right triangle.
B. It is isosceles.
C. It is equilateral.
D. It is scalene
E. It is equiangular.
C(8, 6)
x₁
X
8 mi

Answer 1

Yes, the triangle is a right triangle. Verified through vertex coordinates and the Pythagorean Theorem, confirming equal side lengths and a 90-degree angle at C, consistent with option A.

The triangle depicted in the image can be identified as a right triangle. This conclusion can be reached through this methods:

Examination of Vertex Coordinates

- Vertex A: (3, 3)

- Vertex B: (4, 7)

- Vertex C: (8, 6)

Upon calculating the distances between these vertices, we obtain:

- AB =
`√(( 1^2 + 4^2)) = √(17)`

- AC =
`√( (5^2 + 3^2)) = √(34)`

- BC =
`√( (4^2 + 1^2)) = √(17)`

Notably, AB equals BC, signifying an isosceles triangle. Additionally, the sum of angles in a triangle is invariably 180 degrees. As AB equals BC, the angles at A and B are equivalent. Consequently, the angle at C must be 90 degrees, establishing the triangle as a right triangle.