Linear Coordinate Geometry

Linear Coordinate Geometry

Basics of Linear Coordinate Geometry

• Understanding the basic unit of linear coordinate geometry: the point. A point in this context is a location in space defined by its coordinates.
• Familiarising with the concept of a line. In linear coordinate geometry, a line is an infinite set of points extending in both directions.
• Exploring linear equations. These equations define lines in a two-dimensional space, with the most common form being y = mx + c, where m is the gradient of the line and c is the y-intercept.

Coordinates

• Understanding coordinates and their meaning. An ordered pair (x, y) designates a point in the coordinate plane where x is the horizontal distance and y is the vertical distance from the origin.
• Interpreting the coordinates of a point as distances along the x and y axes and applying the concept of negative distances for points left or below the origin.

Gradient

• Defining the concept of gradient. The gradient describes how steep a line is; it is the change in the y-coordinate divided by the change in the x-coordinate (often referred to as ‘rise divided by run’: (y2 - y1) / (x2 - x1)).
• Distinguishing between positive and negative gradients, and interpreting a zero gradient or undefined gradient.

Equations of a Line

• Formulating the equation of a line. This equation represents all the coordinates of points that lie on the line.
• Identifying specific types of lines such as horizontal lines (y = c) and vertical lines (x = a).
• Using two points to derive an equation for the line passing through them.

Y-Intercept

• Discovering the y-intercept which is the point at which the line crosses the y-axis. It is represented as c in the equation of a straight line.

Intersecting Lines

• Understanding how to find the intersection of two lines by setting the equations equal to each other and solving for the value of x and y coordinates.
• Distinguishing between parallel lines (never meet, have the same gradient), and perpendicular lines (intersect at a right angle, gradients multiply to -1).

Distance between Two Points

• Applying the distance formula to determine the exact numerical distance between two points on a line.

Midpoint of a Line Segment

• Calculating the midpoint of a line segment as the average of the x-coordinates and the y-coordinates of the two endpoints.