Question

G(1, 1, -2) is the centroid of the triangle ABC and D is the mid point of BC. IfA=(-1,1,-4) then D=​

Answer 1

Given:

• Centroid of the Triangle ABC = G(1, 1, -2)
• Mid point of BC                        = D

To Find: We have to find the value of D.

Now,

                    Let P(X, Y, Z,)

we have,

                       A(-1, 1, -4)

                       G(1, 1, -2)

the formula of centroid,

                           $G = (\frac{X+X_{1} }{3} , \frac{Y+Y_{1} }{3} , \frac{Z+Z_{1} }{3} )$

we have values of

                              $X_{1} = -1\\Y_{1} = 1\\Z_{1} = -4$

now put them in the equation of centroid (G)

                            $G = (\frac{X-1}{3} , \frac{Y+1}{3} , \frac{Z-4}{3} )$

by putting the given value of G(1, 1, -2)

                          $(1, 1, -2)$ = $(\frac{X-1}{3} , \frac{Y+1}{3} , \frac{Z-4}{3} )$

                          $\frac{X-1}{3} = 1 , \frac{Y+1}{3} = 1, \frac{Z-4}{3} = -2$

Now,

                         $\frac{X-1}{3} = 1\\X-1 = 3\\X = 4$

Similarly,

                        $\frac{Y+1}{3} = 1\\Y+1 = 3\\Y = 2\\\\\frac{Z-4}{3} = -2\\Z-4 = -6\\Z = -2$

Now we have values of (x, y, z)

              (x, y, z) = (4, 2, -2)

value of x, y, z divide by 2

                      = (2, 1, -1)

Hence the value of D = (2, 1, -1)