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Question

Find the lengths of the median of ∆ABC whose vertices are A(0, −1), B(2, 1) and C(0, 3).

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Solution

The vertices of ∆ABC are A(0, −1), B(2, 1) and C(0, 3).
Let AD, BE and CF be the medians of ∆ABC.

Let D be the midpoint of BC. So, the coordinates of D are
D2+02,1+32 i.e. D22,42 i.e. D1,2
Let E be the midpoint of AC. So, the coordinates of E are
E0+02,-1+32 i.e. E02,22 i.e. E0,1
Let F be the midpoint of AB. So, the coordinates of F are
F0+22,-1+12 i.e. F22,02 i.e. F1,0
AD = 1-02+2--12 =12+32 = 1+9 = 10 units.BE = 0-22+1-12 =-22+02 = 4+0 = 4 = 2 units.CF = 1-02+0-32 =12+-32 = 1+9 = 10 units.
Therefore, the lengths of the medians: AD = 10 units, BE = 2 units and CF = 10 units

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