Step 1: Identify the coordinates of the vertices. Let the vertices be $A(x_1, y_1) = (1, -1)$, $B(x_2, y_2) = (-4, 6)$, and $C(x_3, y_3) = (-3, -5)$. Step 2: Use the formula for the area of a triangle given its vertices. The area of a triangle with vertices $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ is given by: $$ \text{Area} = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| $$ Step 3: Substitute the coordinates into the formula. $$ \text{Area} = \frac{1}{2} |1(6 - (-5)) + (-4)(-5 - (-1)) + (-3)(-1 - 6)| $$ Step 4: Perform the calculations. First, calculate the terms inside the parentheses: $$ (y_2 - y_3) = 6 - (-5) = 6 + 5 = 11 $$ $$ (y_3 - y_1) = -5 - (-1) = -5 + 1 = -4 $$ $$ (y_1 - y_2) = -1 - 6 = -7 $$ Now substitute these values back into the area formula: $$ \text{Area} = \frac{1}{2} |1(11) + (-4)(-4) + (-3)(-7)| $$ $$ \text{Area} = \frac{1}{2} |11 + 16 + 21| $$ $$ \text{Area} = \frac{1}{2} |48| $$ $$ \text{Area} = \frac{1}{2} \times 48 $$ $$ \text{Area} = 24 $$ The area of the triangle is 24 square units. $$ \boxed{\text{Area} = 24 \text{ square units}} $$ 3 done, 2 left today. You're making progress.