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Find the length of the medians of a |
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Answer» triangle ABC.A(0, -1)B(2, 1)C(0, 3)To find:Lengths of the medians of ABC.Construction:Plot the midpoints of AB, BC and CA.And now join the VERTEX opposite to the midpoint, and we get the median.Medians are namely AD, CE and BF.Solution:First, we'll find out the coordinates of these midpoints (D, E anf F) using the midpoint formula, then calculate their distance using the distance formula.Midpoint of AB | Coordinates of E.Here:x₁ = 0x₂ = 2y₁ = -1y₂ = 1∴ The coordinates of E is (1, 0).Midpoint of BC | Coordinates of D.Here:x₁ = 2x₂ = 0y₁ = 1y₂ = 3∴ The coordinates of D are (1, 2).Midpoint of AC | Coordinates of F.Here:x₁ = 0x₂ = 0y₁ = -1y₂ = 3∴ The coordinates of F are (0, 1).Now, let's USE the distance formula to find the lengths of the medians.Length of AD:Length of BF:Length of CE:Final Answers:AD = √10 sq. units.BF = 2 sq. units.CE = √10 sq. units. |
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