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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Here are the solutions for the requested problems. 1.a) Calculate the inclination of the line joining A(3, -1) and B(-2, -3). Step 1: Calculate the gradient m of the line. m = (y_2 - y_1)/(x_2 - x_1) m = (-3 - (-1))/(-2 - 3) m = (-3 + 1)/(-5) m = (-2)/(-5) m = (2)/(5) Step 2: Calculate the inclination . = m = (2)/(5) = ((2)/(5)) ≈ 21.8014^ Rounded to two decimal places: ≈ 21.80^ The inclination is 21.80^. 1.c) Calculate the inclination of the line joining F(4, 5) and G(4, 9). Step 1: Calculate the gradient m of the line. m = (y_2 - y_1)/(x_2 - x_1) m = (9 - 5)/(4 - 4) m = (4)/(0) The gradient is undefined. Step 2: Determine the inclination . An undefined gradient indicates a vertical line. The inclination of a vertical line is 90^. The inclination is 90^. 2.a) Calculate the gradient of a line with inclination 135^. Step 1: Use the formula m = . m = (135^) m = -1 The gradient is -1. 2.c) Calculate the gradient of a line with inclination 60^. Step 1: Use the formula m = . m = (60^) m = sqrt(3) The gradient is sqrt(3). Send me the next one 📸