Question

If the point $A(3,2,2)$ and $B(5,5,4)$ are equidistant from $P$, which is on $x$ -axis, then the coordinates of $P$ are

• A. $\left(\frac{39}{4},2,0\right)$
• B. $\left(\frac{49}{4},2,0\right)$
• C. $\left(\frac{39}{4},0,0\right)$
• D. $\left(\frac{49}{4},0,0\right)$

Answer 1

Answer: (D)

The point on the $x$ -axis is of the form $P(x,0,0)$.
Since, the points $A$ and $B$ are equidistant from $P$.
Therefore, $P{A}^2=P{B}^2$
i.e.,$(x-3{)}^2+(0-2{)}^2+(0-2{)}^2$
$=(x-5{)}^2+(0-5{)}^2+(0-4{)}^2$
$\Rightarrow 4x=25+25+16-17$ i.e., $x=\frac{49}{4}$
Thus, the point $P$ on the $x$ -axis is $\left(\frac{49}{4},0,0\right)$ which is equidistant from $A$ and $B$.