If the points A(1, 2), B(3, 4), and C(5, 6) are collinear, what is the area of triangle ABC?

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Q: If the points A(1, 2), B(3, 4), and C(5, 6) are collinear, what is the area of triangle ABC?

Solution: Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | = 0.

Steps: 8

Step 1: Understand that collinear points are points that lie on the same straight line.
Step 2: Identify the coordinates of the points A(1, 2), B(3, 4), and C(5, 6).
Step 3: Use the formula for the area of a triangle given by three points (x1, y1), (x2, y2), (x3, y3): Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) |.
Step 4: Substitute the coordinates into the formula: x1 = 1, y1 = 2, x2 = 3, y2 = 4, x3 = 5, y3 = 6.
Step 5: Calculate the expression inside the absolute value: 1(4-6) + 3(6-2) + 5(2-4).
Step 6: Simplify the calculations: 1(-2) + 3(4) + 5(-2) = -2 + 12 - 10 = 0.
Step 7: Since the result is 0, the area of triangle ABC is 1/2 * |0| = 0.
Step 8: Conclude that the area of triangle ABC is 0 because the points are collinear.