Q103 / 160 · AP EAMCET 2020 (17 Sep Shift 2) · Mathematics

If origin is the centroid of the triangle \(P Q R\) with vertices \(P(2 a, 2,6), Q(-4,3 b,-10)\) and \(R(8,14,2 c)\), then the values of \(a, b, c\) respectively are

  • A
    \(2, \frac{16}{3},-2\)
  • B
    \(-2,-\frac{16}{3},-2\)
  • Correct answer
    C
    \(-2,-\frac{16}{3}, 2\)
  • D
    \(-2, \frac{16}{3},-2\)

Solution

Centroid is given by, \(\begin{aligned} & x=\frac{x_1+x_2+x_3}{3} \\ & y=\frac{y_1+y_2+y_3}{3} \\ & z=\frac{z_1+z_2+z_3}{3} \end{aligned}\) Using values given, \(0=\frac{2 a-4+8}{3} \Rightarrow a=-2\) Also, \(\quad 0=\frac{2+3 b+14}{3}, b=\frac{-16}{3}\) and \(\quad 0=\frac{6-10+2 C}{3}, c=2\)

Hence, the correct answer is option: 'C'.

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