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
are of G are (1, -4). 13.2 Calculate the length of CG. Leave your answer in surd form. Step 1: Use the distance formula d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2) with points C(2, 1) and G(1, -4). CG = sqrt((1-2)^2 + (-4-1)^2) Step 2: Simplify the expression. CG = sqrt((-1)^2 + (-5)^2) CG = sqrt(1 + 25) CG = sqrt(26) The length of CG is sqrt(26). 13.3 Calculate the gradient of BC. Step 1: Use the gradient formula m = (y_2-y_1)/(x_2-x_1) with points B(4, -5) and C(2, 1). m_BC = (1 - (-5))/(2 - 4) Step 2: Simplify the expression. m_BC = (1 + 5)/(-2) m_BC = (6)/(-2) m_BC = -3 The gradient of BC is -3. 13.4 Calculate the value of , the angle of inclination of BC, rounded off to ONE decimal digit. Step 1: Use the relationship = m_BC. From 13.3, m_BC = -3. = -3 Step 2: Calculate using the arctangent function. = (-3) ≈ -71.565^ Step 3: Adjust the angle to be between 0^ and 180^ for the angle of inclination. = -71.565^ + 180^ = 108.435^ Step 4: Round the angle to one decimal digit. ≈ 108.4^ The value of is 108.4^. 13.5 Show that ABC is an isosceles triangle. Step 1: Calculate the length of side AB using points A(-2, -3) and $B(4, -