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The centroid of a triangle ABC is at the point `(1, 1, 1)`. If the coordinates of A and B are `(3, 5, 7)`and `(1, 7, 6)`, respectively, find the coordinates of the point C. |
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Answer» Coordinates of a centroid `G(x,y,z)` of a triangle can be given as, `G(x,y,z) = ((x_1+x_2+x_3)/3,(y_1+y_2+y_3)/3,(z_1+z_2+z_3)/3)` Here, coordinates `A(3,-5,7)` and `B(-1,7,-6)` are given and coordinates of centroid `(1,1,1)` are given. We have to find `C(c_1,c_2,c_3)`. `:. (3-1+c_1)/3 = 1=> c_1 = 1` `(-5+7+c_2)/3 = 1=> c_2 = 1` `(7-6+c_3)/3 = 1 => c_3 = 2` So, coordinates of `C` are `(1,1,2)`. |
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