Final answer:
The area of the triangle with coordinates (0,0), (6,8), and (12,0) is 36 square units.
Step-by-step explanation:
To find the area of a triangle with coordinates (0,0), (6,8), and (12,0), we can use the formula for the area of a triangle.
First, we need to calculate the base of the triangle, which is the distance between the points (0,0) and (12,0). By using the distance formula, we find that the base of the triangle is 12 units.
Next, we calculate the height of the triangle. The height is the perpendicular distance from the vertex (6,8) to the base. By drawing a perpendicular line from (6,8) to the base and using the Pythagorean theorem, we can find that the height is 6 units.
Finally, we use the formula for the area of a triangle: Area = 1/2 * base * height. Plugging in the values, we get: Area = 1/2 * 12 * 6 = 36 square units.
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