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
⇒ 6 + x = 0 and 6 + y = -9
⇒ x = -6 and y = -15
Hence, the third vertex of a triangle is (-6, -15)
Text Solution
(0, 4, 2)(0, - 4, 2)(0, 4, - 2)(0, - 4, - 2)
Answer : D