Question

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

It is an equilateral triangle.
It is an equilateral triangle.

It is an scalene triangle.
It is an scalene triangle.

It is an right triangle.
It is an right triangle.

It is an isosceles triangle.

Answer 1

To classify triangle \( \triangle ABC \) formed by the points \( A(3,-2) \), \( B(2,-5) \), and \( C(4,-5) \), we need to calculate the lengths of the sides of the triangle using the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

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

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

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

Now we have the lengths:
- \( AB = \sqrt{10} \)
- \( BC = 2 \)
- \( AC = \sqrt{10} \)

### Classification:
- Since \( AB = AC \), two sides are equal, which means that \( \triangle ABC \) is an isosceles triangle.

Therefore, the correct classification of \( \triangle ABC \) is:

**It is an isosceles triangle.**