Area of Triangle in Coordinate Plane

Easy Problem Solving Geometry

In a coordinate plane, let points A(2, 3), B(6, 7), and C(x, y) form a triangle. What is the area of triangle ABC?

The area of a triangle formed by three points A(x1, y1), B(x2, y2), and C(x3, y3) in the coordinate plane can be calculated using the formula:

$$ ext{Area} =\frac{1}{2} imes |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| $$

Determine if the following statements provide sufficient information to calculate the area of triangle ABC:

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

Both statements (1) and (2) together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

Statements (1) and (2) together are not sufficient.

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