# Find the distance between and when: (i) PQ is parallel to the y-axis,

Question:

Find the distance between $\mathrm{P}\left(x_{1}, y_{1}\right)$ and $\mathrm{Q}\left(x_{2}, y_{2}\right)$ when:

(i) $\mathrm{PQ}$ is parallel to the $y$-axis,

(ii) $\mathrm{PQ}$ is parallel to the $x$-axis.

Solution:

The given points are $\mathrm{P}\left(x_{1}, y_{1}\right)$ and $\mathrm{Q}\left(x_{2}, y_{2}\right)$.

(i) When PQ is parallel to the y-axis, x1 = x2.

In this case, distance between $\mathrm{P}$ and $\mathrm{Q}=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

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

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

(ii) When PQ is parallel to the x-axis, y1 = y2.

In this case, distance between $\mathrm{P}$ and $\mathrm{Q}=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

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

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