Point C divides line segment AB into two parts with lengths in a ratio of 3:2. Let's first calculate the length of AB. Using the distance formula, we get:
AB = √[(7 - (-3))^2 + (6 - 9)^2] = √(10^2 + 3^2) = √109
Let's assume that C divides AB into two parts with lengths 3k and 2k, respectively. Then, we have:
AC = 3k and BC = 2k
Since C is on the line segment AB, we can write:
AC + BC = AB
3k + 2k = √109
5k = √109
k = √109 / 5
Now, we can find the coordinates of point C using the midpoint formula:
C(x, y) = [(3k * x2 + 2k * x1) / (3k + 2k), (3k * y2 + 2k * y1) / (3k + 2k)]
Substituting the given values, we get:
C(x, y) = [(3/5) * 7 + (2/5) * (-3), (3/5) * 6 + (2/5) * 9] = [1.4, 6.6]
Therefore, point C is located at **(1.4, 6.6)**.