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

Here $P(x_1,y_1)$ and $Q(x_2,y_2)$ are two points.

Then $PQ=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

(i) PQ is parallel to the y-axis then $x_2-x_1=0$

Then $PQ=\sqrt{(y_2-y_1{)}^2}=|y_2-y_1|$

(ii) PQ is parallel to the x-axis then $y_2-y_1=0$

Then $PQ=\sqrt{(x_2-x_1{)}^2}=|x_2-x_1|$