## Distance in a Cartesian Coordinate System

 Terms in Coordinates Coordinate A set of values that show an exact position On graphs, it is usually a pair of numbers The first number shows the horizontal distance, and the second number shows the vertical distance Origin A point where horizontal and vertical axes intersect The coordinate of origin always $$(0,0)$$ Scale The ratio of the length in a drawing (graph) to the length of the real thing Cartesian Plane Two perpendicular number lines: the $$x-$$axis, which is horizontal, and the $$y-$$axis, which is vertical that intersect at a right angle $$x-$$axis Horizontal axis and perpendicular to the $$y-$$axis in the Cartesian coordinate system $$y-$$axis Vertical axis and perpendicular to the $$x-$$axis in the Cartesian coordinate system
7.1  Distance in a Cartesian Coordinate System

Distance between two points on the Cartesian plane:

• The right-angled triangle representation method is used whereby the distance can be determined from the scale on the $$x-$$axis and the $$y-$$axis
• Pythagoras theorem is used to calculate the distance $$AB$$, that is,

\begin{aligned} &\space AB^2 = AC^2 +CB^2 \\\\& AB= \sqrt{AC^2 + CB^2} \end{aligned}

The formula if the distance between two points on the plane:

The distance can be determined if,

(i)

Two points have the same $$y-$$coordinate

Distance $$= (x_2 - x_1) \text{unit}$$

(ii)

Two points have the same $$x-$$coordinate

Distance $$= (y_2 - y_1) \text{unit}$$

Distance between two points on a plane:

 Definition Measurement of distance or length between two points.

Formula

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