Write the formula for the area of the triangle having its vertices at `(x_1,\ y_1),\ \ (x_2,\ y_2)` and `(x_3,\ y_3)` .

Find the coordinates 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) .

Show that the coordinates off the centroid of the triangle with vertices A(x_1, y_1, z_1),\ B(x_2, y_2, z_2)a n d\ (x_3, y_3, z_3) are ((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3,(z_1+z_2+z_3)/3)

Write the condition of collinearity of points (x_1,\ y_1),\ \ (x_2,\ y_2) and (x_3,\ y_3) .

Show that the centroid of the triangle with vertices A(x_1,\ y_1,\ z_1) , B(x_2,\ y_2,\ z_2) and A(x_3,\ y_3,\ z_3) has the coordinates (("x"_1+"x"_2+"x"_2)/3,("y"_1+"y"_2+"y"_2,)/3("z"_1+"z"_2+"z"_2)/3)

An equilateral triangle has each side to a. If the coordinates of its vertices are (x_(1), y_(1)), (x_(2), y_(2)) and (x_(3), y_(3)) then the square of the determinat |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)| equals

A triangle has its three sides equal to a , b and c . If the coordinates of its vertices are A(x_1, y_1),B(x_2,y_2) \ a n d \ C(x_3,y_3), show that |[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=(a+b+c)(b+c-a)(c+a-b)(a+b-c)

A triangle has its three sides equal to a , ba n dc . If the coordinates of its vertices are A(x_1, y_1),B(x_2,y_2)a n dC(x_3,y_3), show that |(x_1,y_1,2),(x_2,y_2,2),(x_3,y_3, 2)|^2=(a+b+c)(b+c-a)(c+a-b)(a+b-c)

If (-2,\ 1) is the centroid of the triangle having its vertices at (x ,\ 0),\ (5,\ -2),\ (-8,\ y), then x ,\ y satisfy the relation 3x+8y=0 (b) 3x-8y=0 (c) 8x+3y=0 (d) 8x=3y

Find the area of the triangle formed by the lines y = x, y= 2x, y=3x+4

Find the area of the triangle formed by the lines y = x, y= 2x, y=3x+4