To solve the problem of finding the area of the triangle with vertices at ((0,0)), ((2,0)), and ((0,3)):

Step 1: Identify the base and height

• The points ((0,0)) and ((2,0)) lie on the x-axis, so the base of the triangle is the distance between these two points: (2 - 0 = 2).
• The point ((0,3)) lies on the y-axis, so the height is the vertical distance from this point to the base (x-axis): (3 - 0 = 3).

Step 2: Calculate the area

The area of a triangle is given by:
[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} ]

Substitute the values:
[ \text{Area} = \frac{1}{2} \times 2 \times 3 = 3 ]

Answer: (\boxed{3})

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