Find The Equations Of The Medians Of A Triangle, The Coordinates Of Whose Vertices Are (–1, 6), (–3, –9) And (5, –8).

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Question

Find the equations of the medians of a triangle, the coordinates of whose vertices are (–1, 6), (–3, –9) and (5, –8).

diffcult

Solution

Correct option is

29x + 4y + 5 = 0, 8x – 5y – 21 = 0, 13x + 14y + 47 = 0

Let A(–1, 6), B(–3, –9) and C(5, –8) be the vertices of âˆ†ABC. Let D, Eand F be the mid-points of the sides BC, CA and AB respectively.

i.e., (2, –1)

i.e., (–2, –3/2)

∴ Equation of the median AD = Equation of line through (–1, 6) and is

or 29x + 4y + 5 = 0

Equation of median BE is

i.e., 8x – 5y – 21 = 0

and equation of median CF is

i.e. 13x + 14y + 47 = 0

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