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