Can anyone please explain example 13 of the 12 th chapter, in the miscellaneous section... my query is to how we got the equations like (x+3-1)/3=1
Definition of Centroid of a triangle :
The point through which all the three medians of a triangle pass is called centroid of the triangle and it divides each median in the ratio 2:1.
Centroid Formula:
Centroid of a triangle is given by
where (x1,y1,z1) , (x2, y2,z2) , (x3, y3,z3) be the coordinates of the vertices of the triangle.
In the said query,coordinates of centroid are given and coordinates of two vertices are given.
Now you are asked to find the coordinates of the third vertex.
Consider the coordinates of the third vertex be (x, y, z).
Then by using the centroid formula ,the coordinates of centroid will be
But it is given that the coordinates of centroid are (1, 1, 1)
Hence, on comparing the corresponding coordinates, we get
⇒ 2+x=3 , y+2=3, z+1=3
⇒ x=1, y=1 and z=2
Hence the coordinates of the third vertex are (1,1,2)