Question

please solve this question
Q7 VERY VERY IMP FROM BOARD POINT OF VIEW

Answer 1

Okay! So first things first, you have to assign names for the different x's and y's. Then, we have to know that medians are lines drawn from one vertex of a triangle to a side, such that, the side is bisected. That means, the point where it connects to the side is literally the midpoint.

Now, there will be 3 different medians in a triangle. Let us consider this triangle ABC. In triangle ABC, 
AD, BE and CF are medians.

Let the coordinates of A be (x1,y1), B(x2,y2), C(x3,y3)
Then, let the coordinates of D be (x,y), E(x^1,y^1), F(x^2,y^2) 

Now, we have to find the coordinates of D, E and F. It is simple as they are midpoints. So, by midpoint formula,

x= x2+x3/2 = 2 and y= y2+y3/2 = 0
x^1= x1+x3/2 = -3 and y^1= y1+y3/2 = 3
x^2= x1+x2/2 = 2 and y^2= y1+y2/2 = 1

Now, we have the coordinates. Now, we have to find the lengths of the medians AD, BE and CF. For this, we have to use the distance formula. By using distance formula,

AD= \sqrt{(x-x1)^2 + (y-y1)^2}
     = \sqrt{97} units

Similarly, BE = \sqrt{61} units and CF= \sqrt{2} units

Now, for finding the coordinates of the centroid, it is really simple. The formula is (x1+x2+x3/3) and (y1+y2+y3/3)

The x coordinate of the centroid, thus, is -1
The y coordinate of the centroid is 4/3.