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

 

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