Question

The co-ordinates of centroid of triangle is (6,9) and two vertices are (15,0) and (0, 10); let us find the co-ordinates of third vertex.
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Answer 1

We know that the coordinates of the centroid of a triangle whose angular points are(x1,y1),(x2,y2),(x3,y3)are

(3x1+x2+x3,3y1+y2+y3)

So, the coordinates of the centroid of a triangle whose vertices are  (0, 6), (8, 12) and (8, 0) are

(30+8+8,36+12+0)or,(316,6)

Answer 2

Step-by-step explanation:

Let the vertices of triangle be

A = (x1, y1) = (15, 0) and

B = (x2, y2) = (0, 10) and

C = (x3, y3)

Centroid G = (6, 9)

Centroid of a triangle is given by

G =

⇒ (6, 9) =

Substituting values

⇒ (6, 9) =

Equating x and y coordinates

⇒

= 6 and

= 9

⇒ 15 + x3 = 18 and 10 + y3 = 27

⇒ x3 = 3 and y3 = 17

Hence the coordinates of third vertex is (3, 17)