A triangle has vertices at (1, 2), (4, 6), and (1, 6). What is the area of the t

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Question: A triangle has vertices at (1, 2), (4, 6), and (1, 6). What is the area of the triangle?

Options:

Correct Answer: 6 cm²

Solution:

Area = 1/2 * |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)| = 1/2 * |1(6-6) + 4(6-2) + 1(2-6)| = 1/2 * |0 + 16 - 4| = 1/2 * 12 = 6 cm².

A triangle has vertices at (1, 2), (4, 6), and (1, 6). What is the area of the triangle?

A triangle has vertices at (1, 2), (4, 6), and (1, 6). What is the area of the triangle?

Step 1: Identify the coordinates of the triangle's vertices. They are (1, 2), (4, 6), and (1, 6).
Step 2: Assign the coordinates to variables: Let (x1, y1) = (1, 2), (x2, y2) = (4, 6), and (x3, y3) = (1, 6).
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(6-6) + 4(6-2) + 1(2-6)|.
Step 5: Calculate each part inside the absolute value: 1(6-6) = 1*0 = 0, 4(6-2) = 4*4 = 16, and 1(2-6) = 1*(-4) = -4.
Step 6: Combine the results: Area = 1/2 * |0 + 16 - 4| = 1/2 * |12|.
Step 7: Calculate the final area: Area = 1/2 * 12 = 6 cm².

Area of a Triangle – The formula for calculating the area of a triangle given its vertices using the determinant method.
Coordinate Geometry – Understanding how to apply coordinates of points in a Cartesian plane to geometric formulas.