Two vertices of a triangle are 2, (3, 1) and (5 2 4 its centroid is 1, 2), (3 find the third vertex)

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)` 

Compare individual terms on both the sides -

`(x+1+3)/3=0` 

So,

`x=-4` 

Similarly, 

`(y+2+5)/3=20`

Similarly, 

`(y-1)/3=0`

so, 

`y=1` 

So the co-ordinate of third vertex (3,1)

19

Let the third vertex of a triangle be(x,y)


Here, x1 = 1, x2 = 5, x3 = x


and y1 = 4, y2 = 2, y3 = y


and the coordinates of the centroid is (0, -3)


We know that


Two vertices of a triangle are 2, (3, 1) and (5 2 4 its centroid is 1, 2), (3 find the third vertex)


Two vertices of a triangle are 2, (3, 1) and (5 2 4 its centroid is 1, 2), (3 find the third vertex)


Two vertices of a triangle are 2, (3, 1) and (5 2 4 its centroid is 1, 2), (3 find the third vertex)


Two vertices of a triangle are 2, (3, 1) and (5 2 4 its centroid is 1, 2), (3 find the third vertex)


6 + x = 0 and 6 + y = -9


x = -6 and y = -15


Hence, the third vertex of a triangle is (-6, -15)


Two vertices of a triangle are 2, (3, 1) and (5 2 4 its centroid is 1, 2), (3 find the third vertex)

Text Solution

(0, 4, 2)(0, - 4, 2)(0, 4, - 2)(0, - 4, - 2)

Answer : D