If the coordinates of the vertices of a triangle are (0,0), (4,0), and (0,3), wh

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Question: If the coordinates of the vertices of a triangle are (0,0), (4,0), and (0,3), what is its area?

Options:

Correct Answer: 6 cm²

Solution:

The area of a triangle can be calculated using the formula A = 1/2 * base * height. Here, base = 4 cm and height = 3 cm, so A = 1/2 * 4 * 3 = 6 cm².

If the coordinates of the vertices of a triangle are (0,0), (4,0), and (0,3), what is its area?

If the coordinates of the vertices of a triangle are (0,0), (4,0), and (0,3), what is its area?

Step 1: Identify the coordinates of the triangle's vertices. They are (0,0), (4,0), and (0,3).
Step 2: Determine the base of the triangle. The base is the distance between the points (0,0) and (4,0), which is 4 units.
Step 3: Determine the height of the triangle. The height is the distance from the point (0,3) straight down to the base (line y=0), which is 3 units.
Step 4: Use the area formula for a triangle: A = 1/2 * base * height.
Step 5: Substitute the values into the formula: A = 1/2 * 4 * 3.
Step 6: Calculate the area: A = 1/2 * 12 = 6.
Step 7: Conclude that the area of the triangle is 6 cm².

Area of a Triangle – The area of a triangle can be calculated using the formula A = 1/2 * base * height, where the base and height are perpendicular to each other.
Coordinate Geometry – Understanding how to determine the base and height of a triangle given its vertices in a coordinate plane.