# 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

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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Various Forms of Equations of line45 mins
Slope, inclination and angle between two lines48 mins
Interactive Quiz on Equations of line23 mins
Parametric Equations of Straight line48 mins
Straight line | Analyse your learning through quiz56 mins
General Equation of a line43 mins
Motion in a Straight Line - 0665 mins
Motion in a Straight Line - 0556 mins
Motion in a Straight Line - 0372 mins
Motion in a Straight Line - 1169 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses