What is Coordinate Geometry?
**Coordinate geometry** (also known as analytic geometry) is a branch of geometry where positions of points are described using **coordinates**. It connects algebra and geometry by allowing you to represent geometric shapes (like lines, circles, and polygons) using algebraic equations. The foundation of coordinate geometry is the **Cartesian plane** (or coordinate plane), which is a grid with a horizontal **x-axis** and a vertical **y-axis**.
There are a few key formulas you'll need to know:
- **Distance Formula**: Find the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
- **Midpoint Formula**: Find the midpoint of a line segment between two points: $$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$
- **Slope Formula**: Find the slope (steepness) of a line between two points: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$
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Video: The Cartesian Plane & Key Formulas!
Watch this video to visualize these fundamental concepts and see how to apply the formulas! 🎥
Practice Problems
Use the formulas to find the missing values!
1) Find the distance between (1, 2) and (4, 6).
2) Find the midpoint of the segment from (3, 5) to (9, 1). (e.g. 6,3)
3) What is the slope of the line passing through (-1, 2) and (3, 4)?
4) What is the equation of a line with slope 2 and y-intercept 3?
⚡ Coordinate Geometry Speed Quiz
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