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: Identify the given points. The two points are A = (-12, 2) and B = (-10, 0). Let (x_1, y_1) = (-12, 2) and (x_2, y_2) = (-10, 0). Step 2: Recall the distance formula between two points. The distance d between two points (x_1, y_1) and (x_2, y_2) is given by: d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2) Step 3: Substitute the coordinates of points A and B into the distance formula. d = sqrt((-10 - (-12))^2 + (0 - 2)^2) Step 4: Simplify the terms inside the parentheses. d = sqrt((-10 + 12)^2 + (-2)^2) d = sqrt((2)^2 + (-2)^2) Step 5: Calculate the squares. d = sqrt(4 + 4) Step 6: Add the terms under the square root. d = sqrt(8) Step 7: Simplify the square root. d = sqrt(4 × 2) d = sqrt(4) × sqrt(2) d = 2sqrt(2) The length of the straight line segment AB is 2sqrt(2) units. The final answer is 2sqrt(2).