Question

The point $P$ is on the $y$-axis. If $P$ is equidistant from $(1,2,3)$ and $(2,3,4)$, then $P_y=$

• A. $\frac{15}{2}$
• B. $15$
• C. $30$
• D. $\frac{3}{2}$

Answer 1

The correct option is A $\frac{15}{2}$

Let the point be $(0,y,0)$
Since, it is equidistant from the $2$ points.
$\Rightarrow (1+(y-2{)}^2+9)=(4+(y-3{)}^2+16)$

$\Rightarrow (10+y^2-4y+4)=(20+y^2-6y+9)$

$\Rightarrow y^2-4y+14=y^2-6y+29$

$\Rightarrow 2y=15$
$\Rightarrow y=$ $\frac{15}{2}$