Question

$A=(2,3,0)$ and $B=(2,1,2)$ are two points. If the points P, Q are on the line AB such that AP$=$PQ$=$QB then PQ$=?$

• A. $2\sqrt{2}$
• B. $6\sqrt{2}$
• C. $\sqrt{8/9}$
• D. $\sqrt{2}$

Answer 1

Answer: (C)

$\sqrt{8/9}$

$A=(2,3,0);B=(2,1,2)$

Given $AP=PQ=PB$

$\Rightarrow AB=3AP=3PQ=3PB\Rightarrow PQ=\frac{AB}{3}$

Now ,

$AB=\sqrt{{(2-2)}^2+{(3-1)}^2+{(0-2)}^2}=\sqrt{0+4+4}=2\sqrt{2}=\sqrt{8}\Rightarrow PQ=\frac{\sqrt{8}}{3}=\sqrt{\frac{8}{9}}$