Question

Two vertices of a triangle are (1, 2), (3, 5) and its centroid is at the origin. Find 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 (1, 2) and (3, 5)

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+1+3)/3,(y+2+5)/3) or ((4+x)/3,(7+y)/3)` 

Compare individual terms on both the sides -

`(4+x)/3 = 0

⇒ 4 + x = 0

⇒ x = -4

and

`(7+y)/3=0`

⇒ 7 + y = 0

⇒ y = -7

So the co-ordinate of third vertex (-4, -7)