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:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
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Calculating the length of side AB: \[ AB = \sqrt{(2 - 3)^2 + (-5 - (-2))^2} = \sqrt{(-1)^2 + (-3)^2} = \sqrt{1 + 9} = \sqrt{10} \]
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Calculating the length of side BC: \[ BC = \sqrt{(4 - 2)^2 + (-5 - (-5))^2} = \sqrt{(2)^2 + (0)^2} = \sqrt{4} = 2 \]
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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.
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