This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
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: Area = (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. Area = (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: Area = (1)/(2) |1(11) + (-4)(-4) + (-3)(-7)| Area = (1)/(2) |11 + 16 + 21| Area = (1)/(2) |48| Area = (1)/(2) × 48 Area = 24 The area of the triangle is 24 square units. Area = 24 square units 3 done, 2 left today. You're making progress.