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

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Let the points be $$ A(-3,5) $$ and $$ B(2,7) $$.

1. Compute the change in the $$ x $$ and $$ y $$ coordinates:
   $$
   \Delta x = 2 - (-3) = 5, \quad \Delta y = 7 - 5 = 2.
   $$

2. The slope $$ m $$ of the line joining $$ A $$ and $$ B $$ is:
   $$
   m = \frac{\Delta y}{\Delta x} = \frac{2}{5}.
   $$

3. The angle $$ \theta $$ that the line makes with the positive $$ x $$-axis is given by:
   $$
   \theta = \tan^{-1}\left(\frac{2}{5}\right).
   $$

4. If an approximate degree measure is desired, compute:
   $$
   \theta \approx \tan^{-1}\left(0.4\right) \approx 21.8^\circ.
   $$

Thus, the line joining the points $$ A $$ and $$ B $$ makes an angle of
$$
\theta = \tan^{-1}\left(\frac{2}{5}\right)
$$
with the positive $$ x $$-axis, which is approximately $$ 21.8^\circ $$.
The line joining points $$ A(-3,5) $$ and $$ B(2,7) $$ makes an angle of approximately $$ 21.8^\circ $$ with the positive $$ x $$-axis.

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

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