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If $(p, q)$ is the point on the $x$ -axis equidistant from the points $(1,2)$ and $(2,3)$, then which one of the following is correct?
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Verified Answer
The correct answer is:
$p=4, q=0$
Since $(p, q)$ is the point on the $\mathrm{x}$ -axis $\therefore q=0$
Let $P=(p, 0)$
$A=(1,2)$ and $B=(2,3)$
Given: $P A=P B$ $\Rightarrow P A^{2}=P B^{2}$
$\Rightarrow(1-p)^{2}+4=(2-p)^{2}+9$
$\Rightarrow 1+p^{2}-2 p-4-p^{2}+4 p=5$
$\Rightarrow 2 p=8$
$\Rightarrow p=4$
Hence, $p=4, q=0$
Let $P=(p, 0)$
$A=(1,2)$ and $B=(2,3)$
Given: $P A=P B$ $\Rightarrow P A^{2}=P B^{2}$
$\Rightarrow(1-p)^{2}+4=(2-p)^{2}+9$
$\Rightarrow 1+p^{2}-2 p-4-p^{2}+4 p=5$
$\Rightarrow 2 p=8$
$\Rightarrow p=4$
Hence, $p=4, q=0$
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