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
Here are the solutions to the problems. Problem (b): Given point A = (4, 1) and vector AB = -3 \\ 1 . We need to find the coordinates of point B. Step 1: Understand the relationship between points and vectors. If A = (x_A, y_A) and B = (x_B, y_B), then the vector AB is given by x_B - x_A \\ y_B - y_A . Step 2: Set up equations for the coordinates of B. We have A = (4, 1), so x_A = 4 and y_A = 1. We are given AB = -3 \\ 1 . Therefore, we can write: x_B - 4 \\ y_B - 1 = -3 \\ 1 This gives two separate equations: x_B - 4 = -3 y_B - 1 = 1 Step 3: Solve for x_B and y_B. For the x-coordinate: x_B - 4 = -3 x_B = -3 + 4 x_B = 1 For the y-coordinate: y_B - 1 = 1 y_B = 1 + 1 y_B = 2 The coordinates of B are (1, 2). Problem (c): The line y = 3x - 2 crosses the y-axis at G. We need to write down the coordinates of G. Step 1: Recall the condition for a line crossing the y-axis. A line crosses the y-axis when the x-coordinate is 0. Step 2: Substitute x=0 into the equation of the line. Substitute x=0 into y = 3x - 2: y = 3(0) - 2 Step 3: Calculate the corresponding y-value. y = 0 - 2 y = -2 Step 4: Write down the coordinates of G. Since x=0 and y=-2, the coordinates of G are (0, -2). The coordinates of G are (0, -2). What's next?