Question

If the distance between the points $(4,p)$ and $(1,0)$ is $5$, then the value of $p$ is:

• A. $4$ only
• B. $\pm 4$
• C. $-4$ only
• D. $0$

Answer 1

The correct option is B $\pm 4$

The given points are $(1,0)$ and $(4,p)$

$d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$\Rightarrow 5=\sqrt{(4-1{)}^2+p^2}$

$\Rightarrow 25=(4-1{)}^2+p^2$

$\Rightarrow 25-9=p^2$

$\Rightarrow p^2=16$

$\Rightarrow p=+4,-4$