Geometry

Study of shapes, sizes, properties of space, and geometric relationships.

Points, Lines, and AnglesPolygons and CirclesPerimeter, Area, and Volume
Transformations and SymmetryCoordinate GeometrySolid Geometry
Geometry in Art and DesignGeometry in SportsGeometry in Construction and Engineering
Drawing and VisualizingChecking with Formulas
Points, Lines, and A...Polygons and CirclesPerimeter, Area, and...Transformations and ...Coordinate GeometrySolid GeometryGeometry in Art and ...Geometry in SportsGeometry in Construc...Drawing and Visualiz...Checking with Formul...
Advanced Topics

Coordinate Geometry

Placing Shapes on a Grid

Coordinate geometry (or analytic geometry) uses numbers to describe shapes and their positions. It's like giving every spot on a map an address!

The Coordinate Plane

The plane is made of two number lines:

  • The x-axis (horizontal)
  • The y-axis (vertical)

Each point is given as \( (x, y) \).

Plotting Shapes

By plotting points, we can draw shapes like triangles, rectangles, or circles.

Distance and Midpoint

  • Distance Formula: To find the distance between two points:
    \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)
  • Midpoint Formula:
    \( M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \)

Why Use It?

Coordinate geometry helps in mapping, navigation, and computer graphics.

Key Formula

\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]

Examples

  • Finding the shortest path between two cities on a map.

  • Plotting a triangle using three points: (0,0), (3,0), (0,4).

In a Nutshell

Coordinate geometry puts shapes on grids using numbers.

Key Terms

Coordinate Plane
A grid formed by two perpendicular number lines.
Distance Formula
A way to calculate the distance between two points.
Next
Solid Geometry