Q. 44.7( 3 Votes )
Find the equations of the medians of a triangle, the equations of whose sides are :
3x + 2y + 6 = 0, 2x – 5y + 4 = 0 and x – 3y – 6 = 0
Answer :
Given: equations are as follows:
3x + 2y + 6 = 0 … (1)
2x − 5y + 4 = 0 … (2)
x − 3y − 6 = 0 … (3)
Assuming:
In triangle ABC, let equations (1), (2) and (3) represent the sides AB, BC and CA, respectively.
Concept Used:
Point of intersection of two lines.
Explanation:
Solving (1) and (2):
x = −2, y = 0
Thus, AB and BC intersect at B (−2, 0).
Solving (1) and (3):
x = - 6/11, y = - 24/11
Thus, AB and CA intersect at 
Similarly, solving (2) and (3):
x = −42, y = −16
Thus, BC and CA intersect at C (−42, −16).
Let D, E and F be the midpoints the sides BC, CA and AB, respectively. Then,
Then, we have:
Now, the equation of the median AD is
⇒ 16x – 59y – 120 = 0
The equation of the median BE is
⇒ 25x – 53y + 50 = 0
And, the equation of median CF is
⇒ 41 x – 112 y – 70 = 0
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