In triangle ABC, if the coordinates of A, B, and C are (1, 2), (4, 6), and (7, 2

In triangle ABC, if the coordinates of A, B, and C are (1, 2), (4, 6), and (7, 2) respectively, what is the area of triangle ABC?

In triangle ABC, if the coordinates of A, B, and C are (1, 2), (4, 6), and (7, 2) respectively, what is the area of triangle ABC?

Step 1: Identify the coordinates of the points A, B, and C. A is (1, 2), B is (4, 6), and C is (7, 2).
Step 2: Assign the coordinates to variables: Let x1 = 1, y1 = 2 (for point A), x2 = 4, y2 = 6 (for point B), and x3 = 7, y3 = 2 (for point C).
Step 3: Use the area formula for a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3): Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) |.
Step 4: Substitute the values into the formula: Area = 1/2 | 1(6-2) + 4(2-2) + 7(2-6) |.
Step 5: Calculate each part inside the absolute value: 1(6-2) = 1*4 = 4, 4(2-2) = 4*0 = 0, and 7(2-6) = 7*(-4) = -28.
Step 6: Add these results together: 4 + 0 - 28 = -24.
Step 7: Take the absolute value: |-24| = 24.
Step 8: Multiply by 1/2 to find the area: Area = 1/2 * 24 = 12.

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