Explanation:
According to the question, the distance between the points $(4,p)$ and $(1,0)=5$
i.e.,
$ \displaystyle \sqrt{{{{{(1-4)}}^{2}}+{{{(0-p)}}^{2}}}}=5$
$[\because$ distance between the points $ \displaystyle {{x}_{1}},{{y}_{1}}$ and $ \displaystyle {{x}_{2}},{{y}_{2}}$, d= $ \displaystyle \sqrt{{{{{\left( {{{x}_{2}}-{{x}_{1}}} \right)}}^{2}}+{{{\left( {{{y}_{2}}-{{y}_{1}}} \right)}}^{2}}}}$​]
$ \displaystyle \begin{array}{l}\Rightarrow \sqrt{{{{{(-3)}}^{2}}+{{p}^{2}}}}=5\\\Rightarrow \sqrt{{9+{{p}^{2}}}}=5\end{array}$​
On squaring both the sides, we get
​9 + p² = 25
⇒ p² = 16 ⇒ p = ±4​
Hence, the required value of $p$ is $\pm 4$ .