Question

Two vertices of a triangle have coordinates (–8, 7) and (9, 4). If the centroid of the triangle is at the origin, what are the coordinates of the third vertex?

Answer 1

We have to find the co-ordinates of the third vertex of the given triangle. Let the co-ordinates of the third vertex be (x, y).

The co-ordinates of other two vertices are (−8, 7) and (9, 4)

The co-ordinate of the centroid is (0, 0)

We know that the co-ordinates of the centroid of a triangle whose vertices are `(x_1, y_1), (x_2, y_2), (x_3, y_3)` is-

`((x_1 + x_2 + x_3)/3, (y_1 + y_2 + y_3)/3)`

So,

`(0, 0) = ((x - 8 + 9)/3, (y + 7 + 4)/3)`

Compare individual terms on both the sides-

`(x + 1 )/3 = 0`

So,

x = -1

Similarly,

`(y + 11)/3 = 0`

So,

y = -11

So the co-ordinate of third vertex (-1, -11)