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
Step 1: Find the distance between the points (3, 7) and (5, 8). The distance formula between two points (x_1, y_1) and (x_2, y_2) is: D = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2) Given points are (x_1, y_1) = (3, 7) and (x_2, y_2) = (5, 8). Substitute the coordinates into the distance formula: D = sqrt((5 - 3)^2 + (8 - 7)^2) D = sqrt((2)^2 + (1)^2) D = sqrt(4 + 1) D = sqrt(5) The distance between the points is sqrt(5). Step 2: Find the mid-point of the points (3, 7) and (5, 8). The midpoint formula for two points (x_1, y_1) and (x_2, y_2) is: M = ((x_1 + x_2)/(2), (y_1 + y_2)/(2)) Given points are (x_1, y_1) = (3, 7) and (x_2, y_2) = (5, 8). Substitute the coordinates into the midpoint formula: M = ((3 + 5)/(2), (7 + 8)/(2)) M = ((8)/(2), (15)/(2)) M = (4, (15)/(2)) The midpoint of the points is (4, (15)/(2)). a) The distance between the points is sqrt(5). b) The mid-point of the points is (4, (15)/(2)).