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
Welcome back — been a while! Let's pick up where you left off. To find the distance between two points M and N, we use the distance formula. Step 1: Identify the coordinates of points M and N. Given points are M(-3, 8) and N(5, -7). Let (x_1, y_1) = (-3, 8) and (x_2, y_2) = (5, -7). Step 2: Apply the distance formula. The distance formula is given by: MN = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2) Step 3: Substitute the coordinates into the formula. MN = sqrt((5 - (-3))^2 + (-7 - 8)^2) Step 4: Simplify the terms inside the parentheses. MN = sqrt((5 + 3)^2 + (-15)^2) MN = sqrt((8)^2 + (-15)^2) Step 5: Square the terms. MN = sqrt(64 + 225) Step 6: Add the squared terms. MN = sqrt(289) Step 7: Calculate the square root. MN = 17 The distance MN is 17 units. Comparing this with the given options: (a) 8 units (b) 11 units (c) 15 units (d) 17 units The correct option is (d). The final answer is 17 units. Send me the next one 📸