# 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? - Mathematics

Short Note

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?

#### Solution

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 )

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 6 Co-Ordinate Geometry
Q 13 | Page 62