213k views
1 vote
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

1 Answer

3 votes

Final answer:

Triangle ABC is isosceles because it has two equal sides (AB and BC). It is not a right triangle, equilateral, or equiangular. The correct option for ∆ABC's features is that it is isosceles and scalene.

Step-by-step explanation:

Identifying the Features of ∆ABC

To determine the features of triangle ABC (or ∆ABC), we must examine the given coordinates of its vertices: A(3, 3), B(4, 7), and C(8, 6). By calculating the distances between these points, we can identify the type of triangle and its characteristics.

Step 1: Calculate the distance between each pair of points to determine the lengths of the sides of ∆ABC.

• AB can be found using the distance formula, resulting in AB = √[(4-3)^2 + (7-3)^2] = √[1^2 + 4^2] = √17

• BC can be found similarly, giving us BC = √[(8-4)^2 + (6-7)^2] = √[4^2 + (-1)^2] = √17

• Finally, AC = √[(8-3)^2 + (6-3)^2] = √[5^2 + 3^2] = √34

Since AB = BC, we have two equal sides, which makes ∆ABC isosceles. Also, since AC is not equal to AB or BC, ∆ABC cannot be equilateral.

Step 2: Check for right angles. Using the Pythagorean theorem, we analyze the lengths to see if ∆ABC is a right triangle.

• If ∆ABC were right, then AB^2 + BC^2 should equal AC^2.

• However, (√17)^2 + (√17)^2 does not equal (√34)^2.

Thus, ∆ABC is not a right triangle, and it is also not equiangular because for a triangle to be equiangular, it must be equilateral, which ∆ABC is not.

Since ∆ABC has no equal angles and only two equal sides, the correct option is:

• B. It is isosceles

• D. It is scalene (since it does not have all sides equal)

User ChangLi
by
8.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.