If a triangle has vertices at (1, 2), (4, 6), and (1, 6), what is its area?

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Question: If a triangle has vertices at (1, 2), (4, 6), and (1, 6), what is its area?

Options:

Correct Answer: 12

Solution:

Area = 0.5 * |(1(6-6) + 4(6-2) + 1(2-6))| = 0.5 * |0 + 16 - 4| = 6.

If a triangle has vertices at (1, 2), (4, 6), and (1, 6), what is its area?

If a triangle has vertices at (1, 2), (4, 6), and (1, 6), what is its area?

Step 1: Identify the coordinates of the triangle's vertices. They are (1, 2), (4, 6), and (1, 6).
Step 2: Use the formula for the area of a triangle given by vertices (x1, y1), (x2, y2), (x3, y3): Area = 0.5 * |(x1(y2-y3) + x2(y3-y1) + x3(y1-y2))|.
Step 3: Substitute the coordinates into the formula. Here, x1 = 1, y1 = 2, x2 = 4, y2 = 6, x3 = 1, y3 = 6.
Step 4: Calculate the expression inside the absolute value: 1(6-6) + 4(6-2) + 1(2-6).
Step 5: Simplify each part: 1(0) + 4(4) + 1(-4) = 0 + 16 - 4.
Step 6: Combine the results: 0 + 16 - 4 = 12.
Step 7: Take the absolute value: |12| = 12.
Step 8: Multiply by 0.5 to find the area: Area = 0.5 * 12 = 6.

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.