ANSWER
(5, 4)
EXPLANATION
We are given that C is the midpoint from A to B.
First, we have to find the coordinates of point C.
To do that, we apply the formula for midpoint of two points:
[tex]C=(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})[/tex]
where (x1, y1) and (x2, y2) are the two points.
The coordinates of A and B are (-3, 8) and (9, 2)
Therefore, the coordinate of C is:
[tex]\begin{gathered} C=(\frac{-3+9}{2},\frac{8+2}{2}) \\ C=(\frac{6}{2},\frac{10}{2}) \\ C=(3,5) \end{gathered}[/tex]
Point D is given to be one-third the distance between C and B.
This means that we want to partition the distance between C and B into 3, where D is the point 1/3 that distance away from C.
To find D, we have to find the difference between the coordinate points of C and B, find 1/3 of that, then, add that to the coordinate of C:
[tex]\begin{gathered} \frac{1}{3}(9-3,2-5)=(\frac{1}{3}\cdot6,\frac{1}{3}\cdot-3) \\ (2,-1) \end{gathered}[/tex]
Adding that to the coordinates of C:
[tex]\begin{gathered} D=(3+2,5+(-1))=(3+2,5-1) \\ D=(5,4) \end{gathered}[/tex]
That is the coordinate of D.
