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: Define the position vectors for the given points. The position vectors are: A = 3 \\ 4 , B = -1 \\ 2 , C = -1 \\ -1 , D = a \\ b Step 2: Use the property of a parallelogram that opposite sides are parallel and equal in length. For a parallelogram ABCD, the vector AB must be equal to the vector DC. AB = B - A = -1 \\ 2 - 3 \\ 4 = -1 - 3 \\ 2 - 4 = -4 \\ -2 DC = C - D = -1 \\ -1 - a \\ b = -1 - a \\ -1 - b Step 3: Equate the components of AB and DC to find a and b. -4 \\ -2 = -1 - a \\ -1 - b Equating the x-components: -4 = -1 - a a = -1 + 4 a = 3 Equating the y-components: -2 = -1 - b b = -1 + 2 b = 1 Step 4: State the coordinates of D. The coordinates of D are (a, b). D = (3, 1) The coordinates of D are (3, 1). Send me the next one 📸