To find the other endpoint of the line segment when given one endpoint and the midpoint, you can use the midpoint formula.
The formula for the midpoint \( M \) of a line segment with endpoints \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
In this case, you have:
- Endpoint \( A(-9, -4) \)
- Midpoint \( M(0, 8) \)
Let the other endpoint be \( B(x, y) \). Using the midpoint formula, we set up the following equations:
\[ \frac{-9 + x}{2} = 0 \quad \text{(1)} \] \[ \frac{-4 + y}{2} = 8 \quad \text{(2)} \]
Now solve these equations.
From equation (1):
\[ -9 + x = 0 \implies x = 9 \]
From equation (2):
\[ -4 + y = 16 \implies y = 20 \]
So, the other endpoint \( B \) is:
\[ (9, 20) \]
Thus, the answer is:
(9, 20)
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