__6.1 Distance between Two Points__

*(*

**A***x*,

_{1}*y*) and

_{1}

**C***(x*are two points on a coordinate plane as shown below.

_{2}, y_{2})_{ }*BC*is parallel to the

*x*-axis and

*AB*is parallel to the

*y*-axis. Hence ∆

*ABC*= 90°.

Distance between Point

*A*and*C*=**Example:**

Find the distance between the points

*P*(2, –2) and*Q*(–4, –5).

*Solution:*Let

*P*(2, –2) = (*x*,_{1}*y*) and_{1 }*Q*(–4, –5) = (*x*,_{2}*y*)._{2 }
$\begin{array}{l}\text{Distanceof}PQ\\ =\sqrt{{\left({x}_{2}-{x}_{1}\right)}^{2}+{\left({y}_{2}-{y}_{1}\right)}^{2}}\\ =\sqrt{{\left(-4-2\right)}^{2}+{\left(-5-\left(-2\right)\right)}^{2}}\\ =\sqrt{36+9}\\ =\sqrt{45}\\ =\sqrt{9\times 5}\\ =3\sqrt{5}\text{or}\left(6.71\right)\end{array}$