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
(a) Calculate the coordinates of M. The problem states that BD is a diameter of the circle and M is the center of the circle. Therefore, M is the midpoint of the line segment BD. Step 1: Identify the coordinates of points B and D. B = (-2, -6) D = (0, 8) Step 2: Use the midpoint formula M = ((x_1+x_2)/(2), (y_1+y_2)/(2)). M = ((-2+0)/(2), (-6+8)/(2)) Step 3: Calculate the coordinates of M. M = ((-2)/(2), (2)/(2)) M = (-1, 1) The coordinates of M are M(-1, 1) (b) Find the equation of the line parallel to BD and passing through the point A. Step 1: Calculate the gradient (slope) of the line BD. The coordinates are B(-2, -6) and D(0, 8). The gradient m = (y_2 - y_1)/(x_2 - x_1). m_BD = (8 - (-6))/(0 - (-2)) m_BD = (8 + 6)/(0 + 2) m_BD = (14)/(2) m_BD = 7 Step 2: Determine the gradient of the line parallel to BD. Since the required line is parallel to BD, it will have the same gradient. So, m_parallel = 7. Step 3: Use the point-slope form of a linear equation, y - y_1 = m(x - x_1), with point A(-8, 2) and m_parallel = 7. y - 2 = 7(x - (-8)) y - 2 = 7(x + 8) Step 4: Simplify the equation into the form y = mx + c. y - 2 = 7x + 56 y = 7x + 56 + 2 y = 7x + 58 The equation of the line is y = 7x + 58 That's 4 down, 1 left today. Send me the next one 📸