Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Let $\mathrm{B}\equiv \left(x_1,y_1,{\mathrm{z}}_1\right)$ Co-ordinates of centroid $$\begin{array}{c}\equiv \left(\frac{1+x_1+5}{3},\frac{4+y_1-7}{3},\frac{2+{\mathrm{z}}_1+1}{3}\right)\\ \Rightarrow \left(\frac{4}{3},0,\frac{-2}{3}\right)\equiv \left(\frac{6+x_1}{3},\frac{y_1-3}{3},\frac{3+{\mathrm{z}}_1}{3}\right)\\ \Rightarrow x_1=-2,y_1=3,{\mathrm{z}}_1=-5\\ \therefore \mathrm{B}\equiv (-2,3,-5)\\ \text{ Midpoint side }\mathrm{BC}=\left(\frac{-2+5}{2},\frac{3-7}{2},\frac{-5+1}{2}\right)\\ =\left(\frac{3}{2},-2,-2\right)\end{array}$$