Question

In the diagram $MN$ is a straight line on a Cartesian plane. The coordinates of $N$ are $(12,13)$ and ${MN}^2=9$ units. The coordinates of $M$ are:

• A. $(21,13)$
• B. $(12,22)$
• C. $(12,4)$
• D. $(3,13)$

Answer 1

The correct option is D $(3,13)$

(As MN is parallel to 'x' axis \therefore 'y' coordinate not change)

Let $M=(x,13)$

$\sqrt[6]{6(x-12{)}^2+(13-13{)}^2}=9$

$\Rightarrow (x-12{)}^2=9^2\Rightarrow x+12=\pm 9$

$\Rightarrow x=3,21$ (As 'M' is left of N )

$\therefore x=3$