**Question:**

Find the distance between the points $A\left(x_{1}, y_{1}\right)$ and $B\left(x_{2}, y_{2}\right)$, when

(i) $\mathrm{AB}$ is parallel to the $\mathrm{x}$-axis

(ii) $A B$ is parallel to the $y$-axis.

**Solution:**

(i) Given: AB is parallel to the x-axis.

When AB is parallel to the x-axis, the y co-ordinate of A and B will be the same.

i.e., $y_{1}=y_{2}$

Distance

$=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{1}-y_{1}\right)^{2}}$

$\Rightarrow\left|x_{2}-x_{1}\right|$

Therefore the distance between $A$ and $B$ when $A B$ is parallel to $x$-axis is $\left|x_{2}-x_{1}\right|$

(ii) Given: $A B$ is parallel to the $y$-axis.

When $A B$ is parallel to the $y$-axis, the $x$ co-ordinate of $A$ and $B$ will be the same.

i.e., $X_{2}=X_{1}$

Distance

$=\sqrt{\left(x_{1}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

$\Rightarrow\left|y_{2}-y_{1}\right|$

Therefore the distance between $A$ and $B$ when $A B$ is parallel to $y$-axis is $\left|y_{2}-y_{1}\right|$