What is the area of a triangle with vertices at (1, 1), (4, 1), and (1, 5)?

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Question: What is the area of a triangle with vertices at (1, 1), (4, 1), and (1, 5)?

Options:

Correct Answer: 6

Solution:

Area = 1/2 * base * height = 1/2 * (4 - 1) * (5 - 1) = 1/2 * 3 * 4 = 6.

What is the area of a triangle with vertices at (1, 1), (4, 1), and (1, 5)?

What is the area of a triangle with vertices at (1, 1), (4, 1), and (1, 5)?

Step 1: Identify the vertices of the triangle. The vertices are (1, 1), (4, 1), and (1, 5).
Step 2: Determine the base of the triangle. The base is the distance between the points (1, 1) and (4, 1).
Step 3: Calculate the length of the base. The base length is 4 - 1 = 3.
Step 4: Determine the height of the triangle. The height is the vertical distance from the base (y = 1) to the top vertex (1, 5).
Step 5: Calculate the height. The height is 5 - 1 = 4.
Step 6: Use the area formula for a triangle: Area = 1/2 * base * height.
Step 7: Substitute the base and height into the formula: Area = 1/2 * 3 * 4.
Step 8: Calculate the area: Area = 1/2 * 12 = 6.

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