To find the ordered pairs of the three median bisectors, we need to identify the midpoints of the sides of the triangle defined by the vertices given in each option.
Recall that the median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. To find the midpoints, we can use the formula for the midpoint of a line segment defined by two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ \text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Now, let's evaluate the options given one by one to find the ordered pairs of the median bisectors.
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\( 0c = (3, 4), b = (4.5, 4), a = (4, 2) \):
- Midpoint of \( ab \): \[ \text{Midpoint} = \left( \frac{4.5 + 4}{2}, \frac{4 + 2}{2} \right) = \left( 4.25, 3 \right) \]
- Midpoint of \( bc \): \[ \text{Midpoint} = \left( \frac{4.5 + 3}{2}, \frac{4 + 4}{2} \right) = \left( 3.75, 4 \right) \]
- Midpoint of \( ca \): \[ \text{Midpoint} = \left( \frac{3 + 4}{2}, \frac{4 + 2}{2} \right) = \left( 3.5, 3 \right) \]
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\( 0c = (1, 2), b = (7, 5), a = (6, 2) \):
- Midpoint of \( ab \): \[ \text{Midpoint} = \left( \frac{7 + 6}{2}, \frac{5 + 2}{2} \right) = \left( 6.5, 3.5 \right) \]
- Midpoint of \( bc \): \[ \text{Midpoint} = \left( \frac{7 + 1}{2}, \frac{5 + 2}{2} \right) = \left( 4, 3.5 \right) \]
- Midpoint of \( ca \): \[ \text{Midpoint} = \left( \frac{1 + 6}{2}, \frac{2 + 2}{2} \right) = \left( 3.5, 2 \right) \]
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\( 0c = (2.5, 3.5), 6 = (5, 3.5), a = (3.5, 2) \):
- Midpoint of \( ab \): \[ \text{Midpoint} = \left( \frac{5 + 3.5}{2}, \frac{3.5 + 2}{2} \right) = \left( 4.25, 2.75 \right) \]
- Midpoint of \( bc \): \[ \text{Midpoint} = \left( \frac{5 + 2.5}{2}, \frac{3.5 + 3.5}{2} \right) = \left( 3.75, 3.5 \right) \]
- Midpoint of \( ca \): \[ \text{Midpoint} = \left( \frac{2.5 + 3.5}{2}, \frac{3.5 + 2}{2} \right) = \left( 3, 2.75 \right) \]
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\( 0c = (1.5, 1.5), b = (1, 1.5), a = (2.5, 0) \):
- Midpoint of \( ab \): \[ \text{Midpoint} = \left( \frac{1 + 2.5}{2}, \frac{1.5 + 0}{2} \right) = \left( 1.75, 0.75 \right) \]
- Midpoint of \( bc \): \[ \text{Midpoint} = \left( \frac{1 + 1.5}{2}, \frac{1.5 + 1.5}{2} \right) = \left( 1.25, 1.5 \right) \]
- Midpoint of \( ca \): \[ \text{Midpoint} = \left( \frac{2.5 + 1.5}{2}, \frac{0 + 1.5}{2} \right) = \left( 2, 0.75 \right) \]
From this evaluation, none of these calculations return the median bisectors as correct according to the provided points.
However, the choice of medians can simply be deduced from the vertices of triangle and their midpoints, confirming that they meet at a centroid, which is consistent regardless of the triangle dimensions.
Please clarify or provide additional context if needed to address a specific aspect of the median calculations.