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's the solution for question 6a: a) i) Find the equation of AB. Step 1: Calculate the slope m of the line passing through A (-4, 3) and B (2, -6). m = (y_2 - y_1)/(x_2 - x_1) = (-6 - 3)/(2 - (-4)) = (-9)/(2 + 4) = (-9)/(6) = -(3)/(2) Step 2: Use the point-slope form y - y_1 = m(x - x_1) with point A (-4, 3) and m = -(3)/(2). y - 3 = -(3)/(2)(x - (-4)) y - 3 = -(3)/(2)(x + 4) Step 3: Convert the equation to the general form Ax + By + C = 0. 2(y - 3) = -3(x + 4) 2y - 6 = -3x - 12 3x + 2y - 6 + 12 = 0 3x + 2y + 6 = 0 The equation of AB is 3x + 2y + 6 = 0. ii) Calculate |AB|, leaving your answer in the form asqrt(b). Step 1: Use the distance formula D = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2) for points A (-4, 3) and B (2, -6). |AB| = sqrt((2 - (-4))^2 + (-6 - 3)^2) |AB| = sqrt((6)^2 + (-9)^2) Step 2: Simplify the expression. |AB| = sqrt(36 + 81) |AB| = sqrt(117) Step 3: Express sqrt(117) in the form asqrt(b) by finding the largest perfect square factor of 117. 117 = 9 × 13 |AB| = sqrt(9 × 13) = sqrt(9) × sqrt(13) = 3sqrt(13) The length |AB| is 3sqrt(13). Send me the next one 📸