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
1.1 Determine the coordinates of E, the midpoint of PR. Step 1: Use the midpoint formula E = ((x_1 + x_2)/(2), (y_1 + y_2)/(2)). The coordinates of P are (-1, 2) and R are (3, 0). Step 2: Substitute the coordinates into the formula. E = ((-1 + 3)/(2), (2 + 0)/(2)) Step 3: Simplify the expression. E = ((2)/(2), (2)/(2)) E = (1, 1) The coordinates of E are (1, 1). 1.2 Show that a = -2 if the midpoint of QR is (0; -1). Step 1: Use the midpoint formula for Q and R. The coordinates of Q are (-3, a) and R are (3, 0). The midpoint is given as (0, -1). M_QR = ((-3 + 3)/(2), (a + 0)/(2)) Step 2: Simplify the expression for the midpoint. M_QR = ((0)/(2), (a)/(2)) M_QR = (0, (a)/(2)) Step 3: Equate the y-coordinate of the calculated midpoint to the given y-coordinate. (a)/(2) = -1 Step 4: Solve for a. a = -1 × 2 a = -2 Therefore, it is shown that a = -2. 1.3 Determine the gradient of EQ. Step 1: Identify the coordinates of E and Q. From 1.1, E is (1, 1). From 1.2, Q is (-3, -2) (since a = -2). Step 2: Use the gradient formula m = (y_2 - y_1)/(x_2 - x_1). Let (x_1, y_1) = (1, 1) and (x_2, y_2) = (-3, -2). Step 3: Substitute the coordinates into the formula. m_EQ = (-2 - 1)/(-3 - 1) Step 4: Simplify the expression. m_EQ = (-3)/(-4) m_EQ = (3)/(4) The gradient of EQ is (3)/(4). Send me the next one 📸