To find the ordered pairs of the medians of the triangle formed by the points a(4,5), b(1,2), and c(6,2), we need to determine the midpoints of each side of the triangle and then use these midpoints to find the equations for the medians.
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Find the midpoints of each side of the triangle:
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Midpoint of side AB (between points A(4,5) and B(1,2)): \[ M_{AB} = \left( \frac{4 + 1}{2}, \frac{5 + 2}{2} \right) = \left( \frac{5}{2}, \frac{7}{2} \right) = (2.5, 3.5) \]
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Midpoint of side BC (between points B(1,2) and C(6,2)): \[ M_{BC} = \left( \frac{1 + 6}{2}, \frac{2 + 2}{2} \right) = \left( \frac{7}{2}, 2 \right) = (3.5, 2) \]
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Midpoint of side CA (between points C(6,2) and A(4,5)): \[ M_{CA} = \left( \frac{6 + 4}{2}, \frac{2 + 5}{2} \right) = \left( 5, \frac{7}{2} \right) = (5, 3.5) \]
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Determine the points where the medians will meet: The median from vertex A(4,5) to the midpoint of BC(3.5,2), from vertex B(1,2) to the midpoint of CA(5,3.5), and from vertex C(6,2) to midpoint of AB(2.5,3.5) will all intersect at a single point called the centroid.
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Select the answers based on the found midpoints: From the calculations above:
- The median from A goes to (3.5, 2)
- The median from B goes to (5, 3.5)
- The median from C goes to (2.5, 3.5)
Thus, the correct ordered pairs for the median bisectors are:
- \( c = (2.5, 3.5) \)
- \( b = (5, 3.5) \)
- \( a = (3.5, 2) \)
So the correct response is:
c=(2.5,3.5), b=(5,3.5), and a=(3.5,2)
1 answer