Coordinate Geometry – Page 3

6.1 Distance between Two Points

A (x₁, y₁) and C (x₂, y₂)are two points on a coordinate plane as shown below. 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) = (x₁, y₁) and Q (–4, –5) = (x₂, y₂).

\begin{array}{l} Distance of P Q \\ = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}} \\ = \sqrt{{(- 4 - 2)}^{2} + {(- 5 - (- 2))}^{2}} \\ = \sqrt{36 + 9} \\ = \sqrt{45} \\ = \sqrt{9 \times 5} \\ = 3 \sqrt{5} or (6.71) \end{array}