Question

Find the distance between P (x₁, y₁) and Q (x₂, y₂) when (i) PQ is parallel to the y-axis (ii) PQ is parallel to the x-axis.

Answer 1

The given points are $P\left(x_1,y_1\right)\mathrm{and}Q\left(x_2,y_2\right)$.

Distance between P and Q is:

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

(i) When PQ is parallel to the y-axis:

In this case, $x_1=x_2$.

$\therefore PQ=\sqrt{{\left(x_1-x_1\right)}^2+{\left(y_1-y_2\right)}^2}=\left|y_1-y_2\right|$

(ii) When PQ is parallel to the x-axis:

In this case, $y_1=y_2$.

$\therefore PQ=\sqrt{{\left(x_1-x_2\right)}^2+{\left(y_1-y_1\right)}^2}=\left|x_1-x_2\right|$