What are the coordinates of the centroid of the triangle with vertices `(x_1,y_1)` `(x_2,y_2)` and`(x_3,y_3)`

Write the coordinate of the centroid of the triangle whose vertices are (x_1,y_1,z_1) , (x_2,y_2,z_2) and (x_3,y_3,z_3)

suppose that the mid point of the sides BC,CA and AB of a triangle Delta ABC are (5,7,11), (0,8,5) and (2,3,-1) If the vertices of the triangle are A(x_1,y_1,z_1), B(x_2,y_2,z_2) and C(x_3,y_3,z_3) derive nine equations in x_1,x_2,x_3,y_1,y_2,y_3,z_1,z_2, and z_3

If |{:(2a, x _(1), y _(1)), ( 2b, x _(2), y _(2)), (2c, x _(3), y _(3)):}|= (abc)/(2) ne 0, then the area of the triangle whose vertices are ((x _(1))/(a) , ( y _(1))/(a)) , ( (x _(2))/(b), ( y _(2))/( b) ) and ((x _(3))/( c), (y _(3))/( c)) is

If x_(1) , x _(2), x _(3) as well as y _(1), y _(2) , y _(3) are in GP with the same common ratio, then the point (x _(1) , y _(1)) , (x _(2) , y _(2)) and (x_(3) , y _(3)):

Consider the curve 2y=3-x^2 Find the slope of the tangent to this curve at (x_1,y_1) .

(b)The coordinates of the point R which divides the line segment joining P(x1,y1,z1) and Q(x2,y2,z2) internally in the ratio m:n are given by…………

A plane makes intercepts a, b, c at A, B, C on the coordinate axes respectively. If the centroid of the Delta ABC is at (3, 2, 1), then the equation of the plane is a) x + 2y + 3z = 9 b) 2x - 3y - 6z = 18 c) 2x + 3y + 6z = 18 d) 2x + y + 6z = 18

The coordinates of the vertices of a triangle are(-1,5),(3,7),(1,1).Find the coordinates of its centroid.

If A(x_1, y_1), B(x_2, y_2) and C(x_3, y_3) are vertices of an equilateral triangle whose each side is equal to 'a', then prove that, |[x_1, y_1, 2 ],[ x_2, y_2, 2],[ x_3, y_3, 2]|^2=3 a^4