The vértices of a triangle are E(6,-3), D(-5,-3), C(6,-1). What is the coordinate of its centroid?

Answer 1

Centroid of a triangle with vertices (x₁,y₁), (x₂,y₂) , and (x₃,y₃), is given by ((x₁+x₂ +x₃)/ 3, (y₁+y₂+y₃)/3)

Your quick answer, using the formula is ((6-5+6)/3, (-3-3-1)/3) i.e. (7/3, -7/3).

If you were not taught the formula, but you are aware of the fact that centroid divides a median in 2:1 ratio, you can get to this formula easily as follows:

Mid point of DE , say P, is given by ((6-5)/2, (-3-3)/2)i.e (1/2, -3)

Now CP is a median, the centroid G divides it as CG:GP=2:1

G's co-ordinate , say (h,k), is given by

6-h: h-1/2 = 2:1 or 6-h = 2h -1 or h = 7/3

-1-k:k-(-3) = 2 : 1 or -1-k =2k+6 or k =-7/3

If you were not this theorem, then you find the equation of the median CP using coordinates of C and P.

Similarly assume Q as the mid point of CE , Q is given by ((6+6)/2, (-3-1)/2) i.e. (6,-2)

Find the equation of the median DQ using coordinates of D and Q.

Solve the equations of CP and DQ, you will get the coordinate of median