Question

Given the points A(3,−2)
, B(2,−5)
, and C(4,−5)
, classify △ABC
.(1 point)
Responses

It is a scalene triangle.


It is an equilateral triangle

It is an isosceles triangle.


It is a right triangle.

Answer 1

To classify triangle \( \triangle ABC \) with points \( A(3, -2) \), \( B(2, -5) \), and \( C(4, -5) \), we need to determine the lengths of the sides of the triangle and their relationships.

1. **Calculate the distances between points:**

- **Distance AB**:
\[
AB = \sqrt{(2 - 3)^2 + (-5 + 2)^2} = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10}
\]

- **Distance BC**:
\[
BC = \sqrt{(4 - 2)^2 + (-5 + 5)^2} = \sqrt{(2)^2 + (0)^2} = \sqrt{4} = 2
\]

- **Distance CA**:
\[
CA = \sqrt{(4 - 3)^2 + (-5 + 2)^2} = \sqrt{(1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10}
\]

2. **Compare the lengths of the sides:**
- \( AB = \sqrt{10} \)
- \( BC = 2 \)
- \( CA = \sqrt{10} \)

From the calculations, we can see that:
- \( AB = CA \) (both are \( \sqrt{10} \))
- \( BC = 2 \)

Since two sides of the triangle are equal, \( \triangle ABC \) is classified as an **isosceles triangle**.

Thus, the correct response is:

**It is an isosceles triangle.**