Solve problems involving the distance between two points in the Cartesian coordinate system

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

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

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