Question

Two sides of a triangle are 2x-y=0 and x+y=3. If its centroid is (2,3), what is its third side?

Answer 1

Given:

Two sides of a triangle are 2x-y=0 and x+y=3. If its centroid is (2,3)

To find:

What is its third side?

Solution:

From given, we have:

Let the third side be: y = mx + c

the other two sides are y=2x and x+y=3.  

Therefore, one vertex is:(1,2)  

The other two vertices are: [c/(2-m), 2c/(2-m)] & [(3-c)/(m+1), (3m+c((m+1)].  

We get,  

c/(2-m) + (3-c)/(m+1) + 1 = 6

2c/(2-m) + (3m+c)/(m+1) + 2 = 9.  

upon solving the above equations, we get,

c = -9 and m = 5.

The third side is y = 5x - 9.