Year 12 Coordinate Geometry Introduction

NCEA Level 2 Mathematics Building foundations for advanced geometric concepts Connecting algebra and geometry

What is Coordinate Geometry?

Uses coordinates to represent geometric shapes Combines algebraic methods with geometric concepts Allows precise calculations of distances, areas, and relationships Foundation for calculus and advanced mathematics

The Coordinate Plane

Origin (0,0) - the center point X-axis runs horizontally Y-axis runs vertically Four quadrants divide the plane Points written as (x, y) ordered pairs

Plot the Points Activity

Plot these points on your coordinate plane: A(3, 2) B(-1, 4) C(-2, -3) D(0, -1) What shape do they form when connected?

Distance Between Two Points

Uses the Pythagorean theorem Distance formula: d = √[(x₂-x₁)² + (y₂-y₁)²] Always gives a positive result Essential for finding lengths of line segments

Distance Calculation Practice

Find the distance between: Point A(1, 3) and Point B(4, 7) Show your working step by step What is the exact answer? What is the decimal approximation?

Midpoint Formula

Finds the point exactly halfway between two points Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2) Average of x-coordinates and y-coordinates Useful for finding centers and bisecting line segments

Gradient (Slope) of a Line

{"left":"Measures steepness of a line\nGradient = (y₂-y₁)/(x₂-x₁)\nRise over run\nPositive gradient slopes upward","right":"Negative gradient slopes downward\nZero gradient is horizontal\nUndefined gradient is vertical"}

Linear Equations and Their Graphs

Summary and Next Steps

Coordinate plane foundation established Distance and midpoint formulas mastered Gradient concept understood Ready for circles, parabolas, and other curves Applications in real-world problem solving