3. What are the coordinates of the point \( \frac{1}{4} \) of the way from \( A(-6,-3) \) to \( B(10,9) \) ?(

To find the point that is \( \frac{1}{4} \) of the way from \( A(-6, -3) \) to \( B(10, 9) \), we first calculate the vector from \( A \) to \( B \). This vector can be found by subtracting the coordinates of \( A \) from those of \( B \): \[ \text{Vector } AB = B - A = (10 - (-6), 9 - (-3)) = (16, 12). \] Next, we find \( \frac{1}{4} \) of this vector: \[ \frac{1}{4} \text{ of Vector } AB = \left( \frac{1}{4} \cdot 16, \frac{1}{4} \cdot 12 \right) = (4, 3). \] Finally, we add this vector to the coordinates of point \( A \) to find the coordinates of the point that is \( \frac{1}{4} \) of the way from \( A \) to \( B \): \[ \text{Point} = A + \frac{1}{4} \text{ of Vector } AB = (-6, -3) + (4, 3) = (-6 + 4, -3 + 3) = (-2, 0). \] Thus, the coordinates of the point \( \frac{1}{4} \) of the way from \( A \) to \( B \) are \( (-2, 0) \).