Find the area of the triangle formed by the points A(0, 0, 0), B(1, 0, 0), and C

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Question: Find the area of the triangle formed by the points A(0, 0, 0), B(1, 0, 0), and C(0, 1, 0). (2023)

Options:

Correct Answer: 0.5

Exam Year: 2023

Solution:

Area = 0.5 * base * height = 0.5 * 1 * 1 = 0.5 square units.

Find the area of the triangle formed by the points A(0, 0, 0), B(1, 0, 0), and C(0, 1, 0). (2023)

Find the area of the triangle formed by the points A(0, 0, 0), B(1, 0, 0), and C(0, 1, 0). (2023)

Step 1: Identify the points of the triangle. The points are A(0, 0, 0), B(1, 0, 0), and C(0, 1, 0).
Step 2: Determine the base of the triangle. The base can be the distance between points A and B, which is 1 unit.
Step 3: Determine the height of the triangle. The height is the distance from point C to the line AB, which is also 1 unit.
Step 4: Use the formula for the area of a triangle: Area = 0.5 * base * height.
Step 5: Substitute the values into the formula: Area = 0.5 * 1 * 1.
Step 6: Calculate the area: Area = 0.5 square units.

Area of a Triangle in 3D – The area of a triangle can be calculated using the formula Area = 0.5 * base * height, where the base and height are perpendicular to each other.
Coordinate Geometry – Understanding how to plot points in a 3D coordinate system and how to derive distances and areas from these points.