To find the area of the acute triangle formed by the points A(-3, 5), B(3, 7), and C(2, 3), we can use the formula for the area of a triangle given by three vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\):
\[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]
Substituting the coordinates of the points A, B, and C into the formula:
- \(A(-3, 5)\): \(x_1 = -3\), \(y_1 = 5\)
- \(B(3, 7)\): \(x_2 = 3\), \(y_2 = 7\)
- \(C(2, 3)\): \(x_3 = 2\), \(y_3 = 3\)
Now, we can plug in the values:
\[ \text{Area} = \frac{1}{2} \left| (-3)(7 - 3) + (3)(3 - 5) + (2)(5 - 7) \right| \]
Calculating each term step-by-step:
- \( (-3)(7 - 3) = -3 \cdot 4 = -12 \)
- \( (3)(3 - 5) = 3 \cdot (-2) = -6 \)
- \( (2)(5 - 7) = 2 \cdot (-2) = -4 \)
So we combine these results:
\[ \text{Area} = \frac{1}{2} \left| -12 - 6 - 4 \right| = \frac{1}{2} \left| -22 \right| = \frac{1}{2} \cdot 22 = 11 \]
The area of the triangle is \( \boxed{11} \) square units.