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
Welcome back MintamFeisolib — missed you this week. Here's the solution to question 13: Given points are P(1, 3), Q(-2, 5), R(1, 7), and S(x, y). a) Step 1: Calculate vector PQ. To find the vector from point A to point B, subtract the coordinates of A from the coordinates of B. PQ = x_Q - x_P \\ y_Q - y_P = -2 - 1 \\ 5 - 3 = -3 \\ 2 Step 2: Calculate vector QR. QR = x_R - x_Q \\ y_R - y_Q = 1 - (-2) \\ 7 - 5 = 1 + 2 \\ 2 = 3 \\ 2 Step 3: Calculate vector PR. PR = x_R - x_P \\ y_R - y_P = 1 - 1 \\ 7 - 3 = 0 \\ 4 The vectors are: PQ = -3 \\ 2 , QR = 3 \\ 2 , PR = 0 \\ 4 b) Step 4: Find the coordinates of S. In a parallelogram PQRS, the opposite sides are parallel and equal in length. Therefore, PS = QR. We have P(1, 3) and S(x, y). PS = x - x_P \\ y - y_P = x - 1 \\ y - 3 From Step 2, we know QR = 3 \\ 2 . Step 5: Equate the components of PS and QR. x - 1 \\ y - 3 = 3 \\ 2 Equating the x-components: x - 1 = 3 x = 3 + 1 x = 4 Equating the y-components: y - 3 = 2 y = 2 + 3 y = 5 The coordinates of S are (4, 5). S = (4, 5) Send me the next one 📸