Coordinate Geometry
Coordinate geometry uses the Cartesian plane to describe the position of points and the properties of lines and shapes using coordinates (x, y).
What You Need to Know
Key Concept Diagram
Points are plotted as (x, y) where x is the horizontal position and y is the vertical position
The midpoint of a line segment is the average of the endpoints: ((x1+x2)/2, (y1+y2)/2)
Distance between two points uses Pythagoras: d = sqrt((x2-x1)^2 + (y2-y1)^2)
The gradient (slope) of a line: m = (y2-y1)/(x2-x1)
Key Vocabulary
Coordinate
An ordered pair (x, y) that locates a point on the Cartesian plane
Midpoint
The exact middle point of a line segment, found by averaging the coordinates
Origin
The point (0, 0) where the x-axis and y-axis intersect
Gradient
The steepness of a line, calculated as rise over run
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the midpoint of the segment joining (2, 4) and (8, 10)?
Question 2
Point A is at (0, 0) and point B is at (3, 4). What is the distance AB?
Question 3
Which point lies on the y-axis?
Key Concepts Summary
- ●Points are plotted as (x, y) where x is the horizontal position and y is the vertical position
- ●The midpoint of a line segment is the average of the endpoints: ((x1+x2)/2, (y1+y2)/2)
- ●Distance between two points uses Pythagoras: d = sqrt((x2-x1)^2 + (y2-y1)^2)
- ●The gradient (slope) of a line: m = (y2-y1)/(x2-x1)