To classify triangle \( \triangle ABC \) formed by the points \( A(3,-2) \), \( B(2,-5) \), and \( C(4,-5) \), we need to determine the lengths of the sides.
-
Calculate the distance between the points:
The distance formula between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
-
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 \( CA \): \[ CA = \sqrt{(4 - 3)^2 + (-5 - (-2))^2} = \sqrt{(1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} \]
-
-
Summary of Side Lengths:
- \( AB = \sqrt{10} \)
- \( BC = 2 \)
- \( CA = \sqrt{10} \)
-
Classifying the Triangle:
- Since \( AB = CA \), the triangle has two sides that are equal, which makes \( \triangle ABC \) an isosceles triangle.
Thus, the correct classification of triangle \( \triangle ABC \) is:
It is an isosceles triangle.
5 answers