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
Okay Pop's, let's tackle the next parts of this problem. 2) Calculate the coordinates of the midpoint of line AC. To find the midpoint of a line segment with endpoints (x_1, y_1) and (x_2, y_2), we use the midpoint formula: M = ((x_1 + x_2)/(2), (y_1 + y_2)/(2)) Step 1: Identify the coordinates of points A and C. Point A is (2, 3), so x_1 = 2 and y_1 = 3. Point C is (4, 6), so x_2 = 4 and y_2 = 6. Step 2: Substitute the coordinates into the midpoint formula. M = ((2 + 4)/(2), (3 + 6)/(2)) Step 3: Simplify the expression. M = ((6)/(2), (9)/(2)) M = (3, 4.5) The coordinates of the midpoint of AC are (3, 4.5). 3) Calculate the gradient of AC. To find the gradient (slope) of a line segment with endpoints (x_1, y_1) and (x_2, y_2), we use the gradient formula: m = (y_2 - y_1)/(x_2 - x_1) Step 1: Identify the coordinates of points A and C. Point A is (2, 3), so x_1 = 2 and y_1 = 3. Point C is (4, 6), so x_2 = 4 and y_2 = 6. Step 2: Substitute the coordinates into the gradient formula. m = (6 - 3)/(4 - 2) Step 3: Simplify the expression. m = (3)/(2) m = 1.5 The gradient of AC is 1.5. That's 2 down. 3 left today — send the next one.