To find the ordered pair for point Y, we can use the midpoint formula, which states that the midpoint M of a line segment connecting points \( X(x_1, y_1) \) and \( Y(x_2, y_2) \) is given by:
\[ M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \]
In this case, we know:
- Midpoint \( M = (2, 8) \)
- Point \( X = (10, 4) \)
Let point \( Y = (x_2, y_2) \). We can set up the equations based on the midpoint coordinates:
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For the x-coordinates: \[ \frac{10 + x_2}{2} = 2 \]
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For the y-coordinates: \[ \frac{4 + y_2}{2} = 8 \]
Now, we can solve these equations one by one.
Starting with the first equation:
\[ \frac{10 + x_2}{2} = 2 \] Multiply both sides by 2: \[ 10 + x_2 = 4 \] Now, subtract 10 from both sides: \[ x_2 = 4 - 10 = -6 \]
Now, solving the second equation:
\[ \frac{4 + y_2}{2} = 8 \] Multiply both sides by 2: \[ 4 + y_2 = 16 \] Now, subtract 4 from both sides: \[ y_2 = 16 - 4 = 12 \]
Thus, point \( Y \) is at \( (-6, 12) \).
The ordered pair for point Y is \( \boxed{(-6, 12)} \).