The points A(1, 1),B(-2, 7),and C(3, -3) are | vedclass

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(A) Calculate the distances between the points using the distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.$AB = \sqrt{(-2 - 1)^2 + (7 - 1)^

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Collinear

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(A) Calculate the distances between the points using the distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.$AB = \sqrt{(-2 - 1)^2 + (7 - 1)^2} = \sqrt{(-3)^2 + 6^2} = \sqrt{9 + 36} = \sqrt{45} = 3\sqrt{5}$.$BC = \sqrt{(3 - (-2))^2 + (-3 - 7)^2} = \sqrt{5^2 + (-10)^2} = \sqrt{25 + 100} = \sqrt{125} = 5\sqrt{5}$.$AC = \sqrt{(3 - 1)^2 + (-3 - 1)^2} = \sqrt{2^2 + (-4)^2} = \sqrt{4 + 16} = \sqrt{20} = 2\sqrt{5}$.Since $AB + AC = 3\sqrt{5} + 2\sqrt{5} = 5\sqrt{5} = BC$,the sum of two distances is equal to the third distance.Therefore,the points $A$,$B$,and $C$ are collinear.

The points $A(1, 1)$,$B(-2, 7)$,and $C(3, -3)$ are . . . . . . .

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