Question

Q(10) Coordinate of centroid of a triangle are (5, -3). If two of its vertices are (1,2) and (2,1) find third vertex.​

Answer 1

Answer:

The answer is (12,-12)

Step-by-step explanation:

The formula is

Centroid of a triangle G(x,y) = (x1 + x2 + x3) / 3 , (y1 + y2 + y3) / 3

where x1 = 1, x2 = 2, x3 = x, y1 = 2, y2 = 1, y3 = y, x = 5 and y = -3

Substituting the values we get,

(5,-3) = (1+2+x) / 3, (2+1+y) / 3

(5,-3) = (3+x) / 3, (3+y) / 3

Now solve for x individually

i.e.

5 = 3 + x / 3

5*3 = 3 + x

15 - 3 = x

12 = x

Now solve for y individually

i.e.

-3 = 3 + y / 3

-3*3 = 3 + y

-9 = 3 + y

-9 - 3 = y

-12 = y

Thus, the third vertex is (12,-12)