Question

Given the points A (3, -2), B (2, -5), and C (4, -5), classify triangle ABC. (1 point)
O It is a right trangle.
Q It is an equilateral trangle.
O It is an isosceles tangle.
© It is a scalene tangle

Answer 1

To classify triangle ABC with the given points A (3, -2), B (2, -5), and C (4, -5), we will first calculate the lengths of the sides of the triangle using the distance formula.

The distance formula is given by:

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

1. **Calculating the length of side AB**:
\[
AB = \sqrt{(2 - 3)^2 + (-5 - (-2))^2} = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10}
\]

2. **Calculating the length of side BC**:
\[
BC = \sqrt{(4 - 2)^2 + (-5 - (-5))^2} = \sqrt{(2)^2 + (0)^2} = \sqrt{4} = 2
\]

3. **Calculating the length of side AC**:
\[
AC = \sqrt{(4 - 3)^2 + (-5 - (-2))^2} = \sqrt{(1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10}
\]

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

Since sides AB and AC are of equal length (\(\sqrt{10}\)), triangle ABC is classified as **isosceles.**

Thus, the answer is:
- It is an isosceles triangle.