Chapter F - Foundations: A Prelude to Functions - Section F.1 The Distance and Midpoint Formulas - F.1 Assess Your Understanding - Page 7: 30

See graph. $AC^2=AB^2+BC^2$, $100\ unit^2$.

Step 1. See graph. Step 2. $AB=\sqrt {(-2-12)^2+(5-3)^2}=\sqrt {200}$, $BC=\sqrt {(12-10)^2+(3+11)^2}=\sqrt {200}$, $AC=\sqrt {(-2-10)^2+(5+11)^2}=\sqrt {400}=20$, Step 3. Check $AC^2=AB^2+BC^2$, thus it is a right triangle, Step 4. $Area=\frac{1}{2}(\sqrt {200})(\sqrt {200})=100\ unit^2$.