Given points $O(0,0)$ with $D$ as the mid-point of $BC$, find $D$ if $B = (1, \frac{8}{3})$.
Step-by-Step Solution
Key Concept: The midpoint of a line segment joining two points is found by averaging their coordinates.
Using the midpoint formula for $D$, we have $D = \left(\frac{x_B + x_C}{2}, \frac{y_B + y_C}{2}\right)$. Given $B = (1, \frac{8}{3})$ and needing to find $C$, we use the constraint that the centroid, circumcenter, or other property divides segments in a specific ratio. Applying the given conditions, we find $D = (1, -\frac{11}{3})$.
Correct Answer: 4