On graph paper, plot the points $A(4, 1)$ and $B(10, 9)$.  

1. What is the distance between points $A$ and $B$? That is, what is $AB$?

   Hint (a):

   What is the length of each side of the slope triangle for the line segment?

   Step (a):

   Use the Pythagorean Theorem.

   $6^2 + 8^2 = AB^2$

2. What are the coordinates of the point that is $\frac { 3 } { 4 }$ of the way from point $A$ to point $B$ on $\overline{AB}$?

3. If point $C$ is at $(10, 1),$ what is $m∠CAB$? Show all work.

   Hint (c):

   $\tan{\angle CAB} = \frac{8}{6}$