1. Let's state the problem: You know the midpoint of a line segment but not the endpoints, and you want to find the coordinates of the two original endpoints. 2. The formula for the midpoint $M$ of a segment with endpoints $A(x_1,y_1)$ and $B(x_2,y_2)$ is: $$M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$$ 3. Given the midpoint $M(x_m,y_m)$, the coordinates satisfy: $$x_m = \frac{x_1 + x_2}{2}, \quad y_m = \frac{y_1 + y_2}{2}$$ 4. To find the endpoints, you need additional information such as the length of the segment or one endpoint. Without that, there are infinitely many pairs of endpoints that share the same midpoint. 5. If you know one endpoint, say $A(x_1,y_1)$, you can find the other endpoint $B(x_2,y_2)$ by rearranging the midpoint formula: $$x_2 = 2x_m - x_1, \quad y_2 = 2y_m - y_1$$ 6. This means the other endpoint is the reflection of the known endpoint across the midpoint. 7. In summary, knowing only the midpoint is not enough to find the two original endpoints uniquely. You need at least one endpoint or the length and direction of the segment.