Analytic geometry

This course is a part of Mathematics I, a 16-course Topic series from Khan Academy.

In analytic geometry, also known as coordinate geometry, we think about geometric objects on the coordinate plane. For example, we can see that opposite sides of a parallelogram are parallel by by writing a linear equation for each side and seeing that the slopes are the same.

This course contains 6 segments:

Distance and midpoints

Find the distance between two points or the midpoint of two points.

Dividing line segments

Think about ratios of lengths of segments between points.

Problem solving with distance on the coordinate plane

Use what you know about distance to solve problems on the coordinate plan like finding the perimeter of a shape or determining if a point is on a circle.

Parallel & perpendicular lines on the coordinate plane

You probably know what parallel and perpendicular lines are. In this tutorial, you will learn how these relationships are expressed on the coordinate plane (spoiler: parallel lines have the same slope, and the product of the slopes of perpendicular lines is always -1).

Equations of parallel & perpendicular lines

Learn all about equations of parallel and perpendicular

Coordinate plane proofs

Prove properties of shapes by putting them on the coordinate plane and then using distances, midpoints, and slopes.