Draw the triangle with vertices A = (2, 2), B = (-1, 3), and C = (0, 0). By regarding it as half of a parallelogram, explain why its area equals area (ABC) = 1 ¦det [_ 2 2 -1 3 Move the third vertex to C = (1, -4) and justify the formula 1 x1 У1 1 2 2 1 1 area (ABC) = det x2 y2 1 = det -1 3 2 2 X3 Уз 1 1 -4 1 }] Hint: Subtracting the last row from each of the others leaves 2 2 1 1 60 16 det -1 3 1 = det -2 7 0 = det -2 7 1 -4 1 1 -41 Sketch A' = (1, 6), B' = (-2, 7), C' = (0, 0) and their relation to A, B, C.

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