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
Given points: Point A (-2, 6) and Point B (10, 8). a) To find the gradient of the line passing through A and B. Step 1: Use the gradient formula m = (y_2 - y_1)/(x_2 - x_1). Let (x_1, y_1) = (-2, 6) and (x_2, y_2) = (10, 8). m = (8 - 6)/(10 - (-2)) Step 2: Calculate the gradient. m = (2)/(10 + 2) m = (2)/(12) m = (1)/(6) b) To find the equation of the beam passing through A and B in the form y = mx + c. Step 1: Use the gradient m = (1)/(6) from part (a) and point A (-2, 6) in the point-slope form y - y_1 = m(x - x_1). y - 6 = (1)/(6)(x - (-2)) y - 6 = (1)/(6)(x + 2) Step 2: Rearrange the equation into y = mx + c form. y - 6 = (1)/(6)x + (2)/(6) y - 6 = (1)/(6)x + (1)/(3) Add 6 to both sides: y = (1)/(6)x + (1)/(3) + 6 y = (1)/(6)x + (1)/(3) + (18)/(3) y = (1)/(6)x + (19)/(3) c) To find the midpoint of the straight line joining A and B. Step 1: Use the midpoint formula M = ((x_1 + x_2)/(2), (y_1 + y_2)/(2)). Let (x_1, y_1) = (-2, 6) and (x_2, y_2) = (10, 8). M = ((-2 + 10)/(2), (6 + 8)/(2)) Step 2: Calculate the coordinates of the midpoint. M = ((8)/(2), (14)/(2)) M = (4, 7) That's 2 down. 3 left today — send the next one.