Advanced Coordinate Geometry
Advanced coordinate geometry extends the study of lines and curves on the Cartesian plane to include circles, locus problems, and geometric proofs using algebra.
What You Need to Know
Key Concept Diagram
The distance formula between (x1,y1) and (x2,y2) is d = sqrt((x2-x1)^2 + (y2-y1)^2)
The midpoint of two points is ((x1+x2)/2, (y1+y2)/2)
The gradient of a line is m = (y2-y1)/(x2-x1)
Two lines are perpendicular when the product of their gradients is -1
A locus is a set of points satisfying a given condition
Key Vocabulary
Locus
The set of all points that satisfy a given geometric condition
Gradient
The slope or steepness of a line, measured as rise over run
Perpendicular
Lines or segments that meet at right angles (90 degrees)
Collinear
Three or more points that lie on the same straight line
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Find the distance between (1, 2) and (4, 6).
Question 2
Two lines have gradients m1 = 3 and m2 = -1/3. They are:
Question 3
What is the midpoint of (0, 4) and (6, 2)?
Key Concepts Summary
- ●The distance formula between (x1,y1) and (x2,y2) is d = sqrt((x2-x1)^2 + (y2-y1)^2)
- ●The midpoint of two points is ((x1+x2)/2, (y1+y2)/2)
- ●The gradient of a line is m = (y2-y1)/(x2-x1)
- ●Two lines are perpendicular when the product of their gradients is -1
- ●A locus is a set of points satisfying a given condition