Question

Find the distance between $P$ $(x_1,y_1)$and $Q$ $(x_2,y_2)$ when

i) $PQ$ is parallel to the $y$-axis,

ii)$PQ$ is parallel to the $x$-axis.

Answer 1

(i) When $PQ$ is parallel to $y$-axis, $x_1=x_2$

Distance between $P$ and $Q$ $=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

$=\sqrt{0+(y_2-y_1{)}^2}$

$=|y_2-y_1|$

(ii) When $PQ$ is parallel to x-axis, $y_1=y_2$

Distance between $P$ and $Q$ $=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

$=\sqrt{(x_2-x_1{)}^2+0}$

$=|x_2-x_1|$