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The area of a triangle is 5 sq. units. T...

The area of a triangle is 5 sq. units. Two. Of its vertices are (2,1) and (3,-2). If the third vertex is `((7)/(2),y),` find the value of y.

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To find the value of \( y \) for the given triangle with vertices \( (2, 1) \), \( (3, -2) \), and \( \left(\frac{7}{2}, y\right) \) with an area of 5 square units, we can use the formula for the area of a triangle based on its vertices. ### Step-by-step Solution: 1. **Area Formula**: The area \( A \) of a triangle with vertices \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) is given by: \[ A = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \] ...
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