Question

The co-ordinates of the centroid of a triangle PQR are (2, –5). If Q = (–6, 5) and R = (11, 8); calculate the co-ordinates of vertex P.

Answer 1

Let co-ordinates of P be (x, y)

And of centroid G are (2, –5)

∴ `2  = (x_1 + x_2 + x_3)/3`

= `(x - 6 + 11)/3`

= `(x + 5)/3`

`=>` x + 5 = 6

∴ x = 6 – 5 = 1

And `-5 = (y_1 + y_2 + y_3)/3`

= `(y + 5 + 8)/3`

= `(y + 13)/3`

`=>` y + 13 = –15

∴ y = –15 – 13

= –28

Hence, co-ordinates of vertex P are (1, –28)