Question

two vertices of a triangle are (0,4)  and (6,0) . if the medians meet at a point (2,0) , find the coordinates of the third vertex

Answer 1

Please Note : The point of intersection of medians of a triangle is known as a centroid!
So in the given question the centroid is at (2,0)

Also note that the formula for calculating the coordinates of the centroid is

x = (x1 + x2 + x3 ) / 3
y = (y1 + y2 + y3) / 3

In the Given Question, x1 = 0, y1 = 4, x2 = 6, y2 = 0, x = 2, y = 0.
To calculate x3 and y3 substitute in the above equations which will give you the values 0 and -4

So the coordinates of the third vertex (0,-4)