What is the area of a triangle with vertices at (0, 0), (6, 0), and (3, 4)?

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Question: What is the area of a triangle with vertices at (0, 0), (6, 0), and (3, 4)?

Options:

Correct Answer: 12

Solution:

Area = 1/2 * base * height = 1/2 * 6 * 4 = 12.

What is the area of a triangle with vertices at (0, 0), (6, 0), and (3, 4)?

What is the area of a triangle with vertices at (0, 0), (6, 0), and (3, 4)?

Step 1: Identify the vertices of the triangle. The vertices are (0, 0), (6, 0), and (3, 4).
Step 2: Determine the base of the triangle. The base is the distance between the points (0, 0) and (6, 0). This distance is 6 units.
Step 3: Determine the height of the triangle. The height is the vertical distance from the point (3, 4) to the base (which is the line y = 0). The height is 4 units.
Step 4: Use the formula for the area of a triangle: Area = 1/2 * base * height.
Step 5: Substitute the values into the formula: Area = 1/2 * 6 * 4.
Step 6: Calculate the area: Area = 1/2 * 6 is 3, and 3 * 4 is 12.
Step 7: Conclude that the area of the triangle is 12 square units.

Area of a Triangle – The area of a triangle can be calculated using the formula: Area = 1/2 * base * height, where the base is the length of one side and the height is the perpendicular distance from the opposite vertex to that base.
Coordinate Geometry – Understanding how to determine the base and height of a triangle given its vertices in a coordinate plane.