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(C) Let the vertices be $A(-2, 2)$,$B(8, -2)$,and $C(-4, -3)$.Calculate the lengths of the sides using the distance formula $d = \sqrt{(x_2 - x_1)^2 +

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Right-angled

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(C) Let the vertices be $A(-2, 2)$,$B(8, -2)$,and $C(-4, -3)$.Calculate the lengths of the sides using the distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$:$AB = \sqrt{(8 - (-2))^2 + (-2 - 2)^2} = \sqrt{10^2 + (-4)^2} = \sqrt{100 + 16} = \sqrt{116}$$BC = \sqrt{(-4 - 8)^2 + (-3 - (-2))^2} = \sqrt{(-12)^2 + (-1)^2} = \sqrt{144 + 1} = \sqrt{145}$$AC = \sqrt{(-4 - (-2))^2 + (-3 - 2)^2} = \sqrt{(-2)^2 + (-5)^2} = \sqrt{4 + 25} = \sqrt{29}$Check for the Pythagorean theorem $a^2 + c^2 = b^2$:$(\sqrt{116})^2 + (\sqrt{29})^2 = 116 + 29 = 145$$(\sqrt{145})^2 = 145$Since $AB^2 + AC^2 = BC^2$,the triangle is a right-angled triangle.

What type of triangle is formed by the vertices $(-2, 2)$,$(8, -2)$,and $(-4, -3)$?

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