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.
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Welcome back Kwanga — missed you this week. Here are the solutions to your analytical geometry problems. 2.1 Determine the coordinates of E. E is the midpoint of line segment AB. The coordinates of A are (5, 0) and B are (7, 6). The midpoint formula is: E = ((x_1+x_2)/(2), (y_1+y_2)/(2)) Step 1: Substitute the coordinates of A and B into the midpoint formula. E = ((5+7)/(2), (0+6)/(2)) Step 2: Calculate the coordinates. E = ((12)/(2), (6)/(2)) E = (6, 3) The coordinates of E are (6, 3). 2.2 Determine the equation of line BA. To find the equation of a line, we need its slope and a point on the line. The coordinates of A are (5, 0) and B are (7, 6). Step 1: Calculate the slope (m) of line BA using the formula m = (y_2-y_1)/(x_2-x_1). m_BA = (6-0)/(7-5) m_BA = (6)/(2) m_BA = 3 Step 2: Use the point-slope form of a linear equation, y - y_1 = m(x - x_1), with point A(5, 0) and slope m_BA=3. y - 0 = 3(x - 5) Step 3: Simplify the equation. y = 3x - 15 The equation of line BA is y = 3x - 15. 2.3 Line BA is parallel to straight line with equation: rx - 3y + 5 = 0. Calculate the value of r. If two lines are parallel, their slopes are equal. Step 1: The slope of line BA is m_BA = 3 (from 2.2). Step 2: Find the slope of the given line rx - 3y + 5 = 0 by rearranging it into the slope-intercept form y = mx + c. rx - 3y + 5 = 0 -3y = -rx - 5 3y = rx + 5 y = (r)/(3)x + (5)/(3) The slope of this line is m_2 = (r)/(3). Step 3: Equate the slopes since the lines are parallel. m_BA = m_2 3 = (r)/(3) Step 4: Solve for r. r = 3 × 3 r = 9 The value of r is 9. Send me the next one 📸