To find the other endpoint of a line segment when you have one endpoint and the midpoint, you can use the midpoint formula. The midpoint \( M \) is calculated as follows:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Where \( (x_1, y_1) \) is one endpoint and \( (x_2, y_2) \) is the other endpoint. In this case:
- Endpoint \( A = (-4, 0) \)
- Midpoint \( M = (8, 3) \)
- Let the other endpoint be \( B = (x, y) \)
Using the coordinates of the midpoint, we can set up the equations:
\[ 8 = \frac{-4 + x}{2} \] \[ 3 = \frac{0 + y}{2} \]
Now, let's solve for \( x \) and \( y \).
Solving for \( x \):
- Multiply both sides of the first equation by 2:
\[ 16 = -4 + x \]
- Add 4 to both sides:
\[ x = 16 + 4 \]
\[ x = 20 \]
Solving for \( y \):
- Multiply both sides of the second equation by 2:
\[ 6 = 0 + y \]
- Hence:
\[ y = 6 \]
Thus, the coordinates of the other endpoint \( B \) are \( (20, 6) \).
Conclusion
The other endpoint of the line segment is \( (20, 6) \).
Answer: (20, 6)