Question

Two vertices of a triangle are (1,2) and (3,5). If the centroid of the triangle is at origin, find the co-ordinates of the third vertex.

Answer 1

Coordinate geometry is the branch of mathematics which deals with the position of an object lying in a plane.

Each  point in cartesian plane has two coordinates X coordinate and Y coordinate.
The X co-ordinate is called the abscissa.
The Y co-ordinate is called the ordinate.

Coordinates X and Y taken together are called coordinates of a point. (x,y) is called an ordered pair.

SOLUTION:

We know that the coordinates of the centroid of a triangle whose vertices  are (x1,y1), (x2,y2), (x3,y3) are:
[x = (x1+x2+x3)/3 , y= (y1+y2+y3)/3]

GIVEN:  Centroid is at the origin i.e. (0,0).

Let third vertex be C (x3,y3).

Here,A (x1= 1 ,y1= 2), B(x2= 3 ,y2= 5), C(x3, y3) , x,= 0 y= 0

Centroid =[(1+3+x3)/3, (2+5+y3)/3) ]

4+x3=0 , 7+y3=0
x3= - 4, y3= - 7
(x3,y3)= (- 4,-7)

Hence the coordinates of third vertex C is (- 4,-7).

HOPE THIS WILL HELP YOU..

Answer 2

Centroid formula:-
X = ( x1 + x2 + x3) / 3
Y = ( y1 + y2 + y3) / 3
So,
X= ( 1 + 3 + x3) / 3
0 = ( 4+x3) / 3
-4 = x3
And
Y= ( 2 + 5 + y3) / 3
0 = (7 + y3) / 3
-7 = y3
Hence, third coordinate of triangle is
(-4,-7)