Question

Find the distance between $P(x_1,y_1)$ and $Q(x_2,y_2)$ when :
$\left(i\right)PQ$ is parallel to the $y-$ axis.
$\left(ii\right)PQ$ is parallel to the $x-$ axis.

Answer 1

(i)
Since $PQ$ is aparallel to $y-$ axis $x_1=x_2$
Distance $PQ=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$
$=\sqrt{(x_2-x_2{)}^2+(y_2-y_2{)}^2}$
$=\sqrt{(y_2-y_1{)}^2}$
$=|y_2-y_1|$ ( $\because$ distance should be positive )

$\left(ii\right)$


Since $PQ$ is aparallel to $y-$ axis $y_1=y_2$
Distance $PQ=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$
$=\sqrt{(x_2-x_1{)}^2+(y_2-y_2{)}^2}$
$=\sqrt{(x_2-x_1{)}^2}$
$=|x_2-x_1|$ ( $\because$ distance should be positive )