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
Right Chimuka, let's go. To find the equation of line AB, we need its slope and a point it passes through. Step 1: Identify the coordinates of the given points. From the diagram, point C is (0, 4) and point D is (6, 0). Point A is on the y-axis at y = -1, so its coordinates are (0, -1). Step 2: Calculate the slope of line CD. 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). For line CD, using C(0, 4) and D(6, 0): m_CD = (0 - 4)/(6 - 0) = (-4)/(6) = -(2)/(3) Step 3: Determine the slope of line AB. The problem states that AB is perpendicular to CD. For two perpendicular lines, the product of their slopes is -1. m_AB · m_CD = -1 m_AB · (-(2)/(3)) = -1 m_AB = (-1)/(-2)3 = (3)/(2) Step 4: Find the equation of line AB. We have the slope m_AB = (3)/(2) and a point A(0, -1) that line AB passes through. We can use the point-slope form of a linear equation, y - y_1 = m(x - x_1). y - (-1) = (3)/(2)(x - 0) y + 1 = (3)/(2)x y = (3)/(2)x - 1 The equation of line AB is y = (3)/(2)x - 1. What's next? 📸