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  • If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (– 4, 3b, –10) and R(8, 14, 2c), then find the values of a, b and c.

3. If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (– 4, 3b, –10) and R (8, 14, 2c), then find the values of a, b, and c.

Answers (1)

best_answer

Given,

Triangle PQR with vertices P (2a, 2, 6),  Q (– 4, 3b, -10) and R (8, 14, 2c),

Now, as we know,

The centroid of  a triangle is given by 

\left (\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3} ,\frac{z_1 +z_2+z_3}{3}\right )

Where coordinates of vertices of the triangle are  (x_1,x_2,x_3),(y_1,y_2,y_3)\:and\:(z_1,z_2,z_3) 

Since Centroid of the triangle, PQR is origin = (0,0,0) 

\left (\frac{2a-4+8}{3},\frac{2+3b+14}{3},\frac{6-10+2c}{3} \right )=(0,0,0)

On equating both coordinates, we get

a=-2,b=\frac{-16}{3}\:and\:c=2

Posted by

Pankaj Sanodiya

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