Question

The value of $k$ when the distance between the points $(3,k)$ and $(4,1)$ is $\sqrt{10}$ is

• A. $3$ or $4$
• B. $-4$ or $-2$
• C. $-4$ or $2$
• D. $4$ or $-2$

Answer 1

The correct option is D $4$ or $-2$

We take the points be $P=(x_1,y_1)=(3,k)$ and $Q=(x_2,y_2)=(4,1)$

$\therefore$ The distance $PQ=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}$

$\Rightarrow PQ=\sqrt{{(3-4)}^2+{(k-1)}^2}=\sqrt{k^2-2k+2}=\sqrt{10}$ ...(Given)

$\Rightarrow k^2-2k+2=10$

$\Rightarrow (k-4)(k+2)=0$

$\Rightarrow k=4$ or $-2$