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.

Explore how the separation between points factors into the distance between them.

Measuring Separation

/courses/coordinate-geometry/separating-points/placing-points/

Separation Between Points

/courses/coordinate-geometry/separating-points/combining-separation/

Combining Separations

/courses/coordinate-geometry/separating-points/closest-point/

The Closest Point

/courses/coordinate-geometry/separating-points/comparing-distance/

Comparing Distance

Estimate the distance between points that have horizontal and vertical separation.

Estimating Distance

/courses/coordinate-geometry/estimating-distance/close-to-multiple-points/

Within a Distance

/courses/coordinate-geometry/estimating-distance/distance-ranges/

Distance Ranges

/courses/coordinate-geometry/estimating-distance/same-distance/

Equal Distance

/courses/coordinate-geometry/estimating-distance/estimating-distance/

Calculate the area of shapes based on their coordinates.

Break complex shapes into pieces in order to find their area.

Measuring Area

/courses/coordinate-geometry/measuring-area/measuring-area/

Rectangle Area

/courses/coordinate-geometry/measuring-area/rectangle-area-with-negatives/

Calculating Side Lengths

/courses/coordinate-geometry/measuring-area/triangle-area/

Triangle Area

/courses/coordinate-geometry/measuring-area/combining-rectangles/

Combining Rectangles

/courses/coordinate-geometry/measuring-area/polygon-area/

Polygon Area

Work with variables in place of coordinates.

Give the area of shapes in terms of variables.

Unknown Values

/courses/coordinate-geometry/unknown-values/distance-expressions/

Distances with Variables

/courses/coordinate-geometry/unknown-values/areas-with-variables/

Rectangle Area Expressions

/courses/coordinate-geometry/unknown-values/triangle-area-expressions/

Triangle Area Expressions

/courses/coordinate-geometry/unknown-values/leaving-the-plane/

Variable Side Lengths

Identify combinations of shapes with a specified area.

Selecting Shapes

/courses/coordinate-geometry/selecting-shapes/selecting-shapes/

/courses/coordinate-geometry/selecting-shapes/selecting-multiple-shapes/

Area Expressions

/courses/coordinate-geometry/selecting-shapes/area-expressions/

Compound Shape Expressions

/courses/coordinate-geometry/selecting-shapes/compound-shape-expressions/

Equating Areas

Use the areas of squares and triangles to prove Pythagoras' Theorem.

Pythagoras

/courses/coordinate-geometry/pythagoras/pythagoras-theorem/

Pythagoras' Theorem

/courses/coordinate-geometry/pythagoras/diagonal-distance/

Direct Distance

/courses/coordinate-geometry/pythagoras/squares/

Squares and Sides

/courses/coordinate-geometry/pythagoras/demonstrating-pythagoras/

Demonstrating Pythagoras

/courses/coordinate-geometry/pythagoras/proving-pythagoras/

Proving Pythagoras

Use Pythagoras' Theorem to find a missing side length.

Calculate the direct distance between points based on their coordinates.

Using Pythagoras

/courses/coordinate-geometry/using-pythagoras/side-lengths/

The Unknown Side

/courses/coordinate-geometry/using-pythagoras/distance-from-origin/

Distance from the Origin

/courses/coordinate-geometry/using-pythagoras/grid-diagonals/

Distance from the Grid

/courses/coordinate-geometry/using-pythagoras/distance-from-coordinates/

Distance from Coordinates

Use coordinates and the areas of shapes to derive Pythagoras' Theorem.

Supercharge your thinking with the language of algebra.

Coordinate Geometry

Level 1Measuring Separation

Level 2Estimating Distance

Level 3Measuring Area

Level 4Unknown Values

Level 5Selecting Shapes

Level 6Pythagoras

Level 7Using Pythagoras

Functions

Course description

Topics covered