1. The problem is: Given the midpoint of a segment, how can we find the two original coordinates of the endpoints? 2. The midpoint formula for two points $A(x_1,y_1)$ and $B(x_2,y_2)$ is: $$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right) = (x_m, y_m)$$ where $(x_m, y_m)$ is the midpoint. 3. To find the original coordinates $x_1, y_1, x_2, y_2$ from the midpoint, you need additional information such as one endpoint or the distance between points. 4. If you know one endpoint, say $A(x_1,y_1)$, and the midpoint $(x_m,y_m)$, you can find the other endpoint $B(x_2,y_2)$ by rearranging the midpoint formula: $$x_2 = 2x_m - x_1$$ $$y_2 = 2y_m - y_1$$ 5. This works because the midpoint is the average of the coordinates, so doubling the midpoint coordinates and subtracting the known endpoint coordinates gives the unknown endpoint. 6. Without any additional information, the two original points cannot be uniquely determined from the midpoint alone. Final answer: If you know one endpoint $(x_1,y_1)$ and the midpoint $(x_m,y_m)$, then the other endpoint is: $$\boxed{(x_2,y_2) = (2x_m - x_1, 2y_m - y_1)}$$