Coordinate Geometry
Use coordinates and the areas of shapes to derive Pythagoras' Theorem.
Separation Between Points
Combining Separations
The Closest Point
Comparing Distance
Level Check
Within a Distance
Distance Ranges
Equal Distance
Estimating Distance
Level Check
Rectangle Area
Calculating Side Lengths
Absolute Values
Triangle Area
Combining Rectangles
Polygon Area
Distances with Variables
Rectangle Area Expressions
Triangle Area Expressions
Variable Side Lengths
Selecting Shapes
Area Expressions
Compound Shape Expressions
Equating Areas
Pythagoras' Theorem
Direct Distance
Squares and Sides
Demonstrating Pythagoras
Proving Pythagoras
The Unknown Side
Distance from the Origin
Distance from the Grid
Distance from Coordinates
Exact Distance
Minimum Distance
Minimum and Maximum Distance
Points on a Circle
Circle Radius
The Equation of a Circle
The Missing Coordinate
Naming Circles
Plotting Circles
Leaving the Origin
Radius from Coordinates
General Circle Equations
Plotting from the Equation
Course description
We'll start by exploring methods to estimate the distance between two points on the coordinate plane. Next we'll use distances on the plane to calculate the area of shapes. Finally, we'll use the area of shapes to derive Pythagoras' Theorem and directly calculate straight-line distances on the plane.
Topics covered
- Estimating distances.
- Computing areas of rectangles and triangles.
- Expressions for areas.
- Deriving and using Pythagoras' Theorem.