Question

A(5, x), B(−4, 3) and C(y, –2) are the vertices of the triangle ABC whose centroid is the origin. Calculate the values of x and y.

Answer 1

Co-ordinates of centroid of ΔABC are (0, 0)

∴ `0 = (x_1 + x_2 + x_3)/3`

= `(5 - 4 + y)/3`

`=> 0 = (y + 1)/3`

`=>` y + 1 = 0

∴ y = –1

Again `0 = (y_1 + y_2 + y_3)/3`

= `(x + 3 - 2)/3`

`=> 0 = (x + 1)/3`

`=>` x + 1 = 0

∴ x = –1

∴ x = –1, y = –1