Coordinate Geometry
Coordinate geometry connects algebra and geometry using the number plane. We find distances, midpoints, and gradients of line segments to describe geometric properties algebraically.
What You Need to Know
Key Concept Diagram
Distance formula: d = sqrt((x2-x1)^2 + (y2-y1)^2)
Midpoint formula: M = ((x1+x2)/2, (y1+y2)/2)
Gradient (slope): m = (y2-y1)/(x2-x1)
Parallel lines have equal gradients; perpendicular lines have gradients that multiply to -1
Key Vocabulary
Gradient
The steepness or slope of a line, calculated as rise over run
Midpoint
The point exactly halfway between two endpoints of a segment
Cartesian plane
The coordinate grid with x-axis (horizontal) and y-axis (vertical)
Origin
The point (0, 0) where the x and y axes intersect
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 from (2, 4) to (8, 10)?
Question 2
What is the gradient of the line through (1, 3) and (5, 11)?
Question 3
What is the distance between (0, 0) and (3, 4)?
Key Concepts Summary
- ●Distance formula: d = sqrt((x2-x1)^2 + (y2-y1)^2)
- ●Midpoint formula: M = ((x1+x2)/2, (y1+y2)/2)
- ●Gradient (slope): m = (y2-y1)/(x2-x1)
- ●Parallel lines have equal gradients; perpendicular lines have gradients that multiply to -1