1 Find the angle that the line joining the points \( A \) and \( B \) makes with the positive direction of the \( x \)-axis. (a) \( A(-3,5), B(2.7) \)

To find the angle that the line joining points \( A(-3,5) \) and \( B(2,7) \) makes with the positive direction of the \( x \)-axis, we first need to calculate the slope (\( m \)) of the line. The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). So, \( m = \frac{7 - 5}{2 - (-3)} = \frac{2}{5} \). The angle \( \theta \) can be found using \( \tan(\theta) = m \), leading to \( \theta = \tan^{-1}\left(\frac{2}{5}\right) \). Use a calculator to find \( \theta \) in degrees, which will give you approximately \( 21.8^\circ \). Make sure to double-check your points since the coordinates provided for point B seemed a little mixed up! Types can happen, and it's always good to verify your inputs before proceeding with calculations—after all, even math can have its off days!