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 |