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 for the remaining parts of question 8: The general formula for the point P(x,y) that divides a line segment joining (x_1, y_1) and (x_2, y_2) in the ratio m:n is: For internal division: P(x,y) = ((m x_2 + n x_1)/(m + n), (m y_2 + n y_1)/(m + n)) For external division: P(x,y) = ((m x_2 - n x_1)/(m - n), (m y_2 - n y_1)/(m - n)) c) (3,4) and (24,16) in the ratio 1:2 internally. Step 1: Identify the given values. (x_1, y_1) = (3,4) (x_2, y_2) = (24,16) m = 1, n = 2 Step 2: Calculate the x-coordinate using the internal division formula. x = (1 × 24 + 2 × 3)/(1 + 2) x = (24 + 6)/(3) x = (30)/(3) x = 10 Step 3: Calculate the y-coordinate using the internal division formula. y = (1 × 16 + 2 × 4)/(1 + 2) y = (16 + 8)/(3) y = (24)/(3) y = 8 The coordinate of the point is (10,8). d) (7,8) and (12,15) in the ratio 3:2 alternatively. Assuming "alternatively" means externally, as it's a common type of division in coordinate geometry problems. Step 1: Identify the given values. (x_1, y_1) = (7,8) (x_2, y_2) = (12,15) m = 3, n = 2 Step 2: Calculate the x-coordinate using the external division formula. x = (3 × 12 - 2 × 7)/(3 - 2) x = (36 - 14)/(1) x = 22 Step 3: Calculate the y-coordinate using the external division formula. y = (3 × 15 - 2 × 8)/(3 - 2) y = (45 - 16)/(1) y = 29 The coordinate of the point is (22,29). Drop the next question.