Question

The coordinate of A is \(100m, 100m\). The coordinate of B is \(50m, 50m\). The bearing of line AB is:

• A. \(45^\circ \)
• B. \(135^\circ \)
• C. \(225^\circ \)
• D. \(315^\circ \)

Hint:

To determine the bearing of a line, always check the quadrant based on the coordinate differences: - First quadrant: \(0^\circ\) to \(90^\circ\) - Second quadrant: \(90^\circ\) to \(180^\circ\) - Third quadrant: \(180^\circ\) to \(270^\circ\) - Fourth quadrant: \(270^\circ\) to \(360^\circ\)

Answer 1

The Correct Option is C

Step 1: Understanding the bearing formula. The bearing of a line from point \(A(x_1, y_1)\) to point \(B(x_2, y_2)\) is given by: \[ \theta = \tan^{-1}  \left( \frac{y_2 - y_1}{x_2 - x_1}  \right) \] 
Step 2: Substituting given values. Coordinates of \(A(100, 100)\) and \(B(50, 50)\), \[ \theta = \tan^{-1}  \left( \frac{50 - 100}{50 - 100}  \right) = \tan^{-1}  \left( \frac{-50} {-50}  \right) = \tan^{-1} (1). \] 
Step 3: Identifying the quadrant. Since both differences are negative (\(x_2 - x_1 <0\) and \(y_2 - y_1 <0\)), the line lies in the third quadrant. Thus, the angle in the third quadrant is: \[ \theta = 180^\circ + 45^\circ = 225^\circ. \]