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, Chimuka, let's tackle this geometry problem. Step 1: Identify the coordinates of points P and Q. P is (0, 4). Q is (-4, 0). Step 2: Calculate the slope of line PQ. The slope m of a line passing through two points (x_1, y_1) and (x_2, y_2) is given by m = (y_2 - y_1)/(x_2 - x_1). Using P(0, 4) and Q(-4, 0): m_PQ = (0 - 4)/(-4 - 0) = (-4)/(-4) = 1 Step 3: Determine the slope of the line perpendicular to PQ. If two lines are perpendicular, the product of their slopes is -1. Let the slope of the required line be m_perp. m_perp · m_PQ = -1 m_perp · 1 = -1 m_perp = -1 Step 4: Find the equation of the straight line. The required line passes through the origin O(0, 0) and has a slope m_perp = -1. Using the point-slope form y - y_1 = m(x - x_1): y - 0 = -1(x - 0) y = -x The equation of the straight line is y = -x. That's 2 down. 3 left today — send the next one.