# Analytic geometry

Contents

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.

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

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.

Think about ratios of lengths of segments between points.

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).

Learn all about equations of parallel and perpendicular

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

You know that a circle can be viewed as the set of all points that whose distance from the center is equal to the radius. In this tutorial, we use this information and the Pythagorean Theorem to derive the equation of a circle.

An optional tutorial where you'll figure out the minimum distance from a point to a given line.