Q56 / 160 · TS EAMCET 2014 · Mathematics

If the line joining $A(1,3,4)$ and $B$ is divided by the point $(-2,3,5)$ in the ratio $1: 3$, then $B$ is

  • Correct answer
    A
    $(-11,3,8)$
  • B
    $(-11,3,-8)$
  • C
    $(-8,12,20)$
  • D
    $(13,6,-13)$

Solution

Using internally ratio formula, $$ \begin{aligned} & (-2,3,5) \\ & =\left(\frac{1 \times x+3 \times 1}{1+3}, \frac{1 \times y+3 \times 3}{1+3}, \frac{1 \times z+3 \times 4}{1+3}\right) \\ \Rightarrow & (2,3,5)=\left(\frac{x+3}{4}, \frac{y+9}{4}, \frac{z+12}{4}\right) \\ \Rightarrow & x+3=-8, y+9=12, z=12=20 \\ \Rightarrow & x=-11, y=+3, z=8 \\ \therefore & \text { Required point }=B(-11,3,8) \end{aligned} $$

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

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